Hmm, yes, that sounds like it. Thanks!
It was published in one of the digest size 'zines, probably Asimov’s or Analog, probably in the 1980’s. It was a noir feel story about a time traveling private eye, he’d get into his time machine that was disguised to look like a garbage can, travel back in time on the behest of clients to go back and fix issues caused by amateur time travelers. He would fund his operations in the past by using his machine to time travel into a bank vault right before a robbery, steal a bunch of cash, and the robbers will get blamed for it. The cash he stole, he’d spend even further back in the past. He had a favorite bar he liked to visit in the past, and every time he finished a case, he’d pop back into that bar the very next night after the last time he visited, no matter how much personal time has gone by for him.
Those were all window dressing for the main plot, when he met another professional time traveler who seemed to come out of nowhere and he had to solve the change in the timeline that allowed his rival to exist.
This might have been a series and I’m conflating elements from different stories.
Know thos one off the top of my head - the Ben Hardy series by Warren Salomon - three stories “Time on My Hands” “Time and Punishment” and “As Time Goes By”
I’m reminded of the posted notice “Time travelers strictly cash”.
The name of a story (and a collection) by Spider Robinson
For me, Salomon’s first story of Ben Hardy, hard-boiled temporal private eye, was about one Delorean shy of having enough boisterous fun that I could completely ignore the inconsistencies in the time-travel model—but even so, I had fun as Ben attempted to restore time to its rightful path for heiress Patricia Wadsworth (and in the process try to figure out the familial relations between himself, Pat, Pat’s parents, the inventor of time travel, and that dastardly lawyer).
They all say that. “Why is it,” I asked her, “you seem to remember the, ah, original sequence? In a reality change, memories are altered along with everything else. How can you be certain that time has been tampered with?” That question usually ends it right there.
P.S I think this one was hard for Google because “De Angelis” is Latin for “of the angels” - and so there’s many false detections
And Google finds many things written by people named De Angelis. I had thought that there was a series of De Angeles board stories, like the Venus Equilateral series. It turns out there was just the one story. Thanks to the Gutenberg link, I re-read it and it held up well. I think a series might have gotten tedious.
Did you try Google books?
I found the same fragment of review in Analog very quickly, but you posted while I was typing my reply.
Thank you!
Arthur C. Clarke, I think, wrote a kinda similar Cold War story about a London thief given a gadget with the power to stop time. His client pays him a huge fee and hands him a list of priceless art treasures to steal. He eventually learns that the client is an alien, or maybe from the future, and that a superbomb test is going to destroy the Earth that day. The client wants to save all that art. The thief realizes that his fee is worthless, and that he can either live to the end of his natural life, all alone in a motionless city, or turn off the gadget and die along with everyone else when the superbomb explodes.
I’ve seen that as an episode of an anthology TV series.
All The Time In The World
By Arthur C. Clarke.
That’s it - thanks!
That reminds me of another very short story I read somewhere where the plot was a scientist invents the ability to pause time, and when time is paused he accidentally slips on a beaker in his lab, hits his head on a table and instantly dies, and time is paused for all of humanity forever.
And now I’m thinking of a different story about a commercial time travel setup, in which the company would take their paying clients back to the age of dinosaurs… no, just kidding. 
This one would have been published in the late 70’s in Asimov’s. A time travel agency where clients would pay for specific changes to the timeline. Which 12-year-old me should have thought WTF, why is that even allowed, but I just accepted it. The main plot involved accepting a job from a man who wanted to rewrite history to keep his son from being killed in Vietnam, and the agent was having a right hard time of it. The agent would dive into the timestream, and effect the changes by possessing people in that time and place. Walk around in their bodies for a time to influence later events.
This had been an established business, making money, but somehow up until this client, they hadn’t figured out that the only time they ever made money was when the agent failed and the company got to keep the retainer. If the agent succeeded, this changed the timestream so the client never contracted the company in the first place. And 12yo me also just accepted this outcome as a neat ending without wondering “Why??” I got better.
When I read the Ben Hardy stories I asked about above, I specifically recalled reading the earlier story, and appreciating that the Ben Hardy stories solved that time travel issue. The detective would take a signed copy of the contract with him, and this gave him the legal right to force the client, who had forgotten ever contracting in the first place, to pay up.
Joking or not, that did happen in Mastodonia, by Clifford D. Simak. They had hunting expeditions in the age of dinosaurs.
This reminds me of something I realized about the TV show Seven Days. They have a time machine that can jump back 7 days, to fix things that went badly, like terrorist attacks and the like. But every jump wipes out the previous timeline.
They make a big thing out of launching the time ship for every mission, like a NASA launch. But that all gets wiped out by changing the past. So the “ground crew” have never actually seen a successful launch of the time ship!
That was also the plot of Ray Bradbury’s A Sound of Thunder but I don’t know which one came first since they both came out in the 1950s.
Yes, Google Books was helpful
“A Sound of Thunder” was published in Collier’s on June 28, 1952. Mastodonia is adapted from his short story “Project Mastodon”, published in Galaxy in March 1955. Wikipedia and Goodreads was what I checked for that. Incidentally, a short story named “Time Patrol” by Poul Anderson, with apparently the same plot, first appeared in The Magazine of Fantasy and Science Fiction in May 1955. The End of Eternity by Isaac Asimov, which was published on August 25, 1955, has a similar plot.