I guess the OP says it. How are touch screens handled in the various worlds and stories where telekinetic characters exist? How is their in/ability to use them discussed or used, if at all?
Can’t recall ever seeing it happen. But a resistive screen would be the easiest to telekenect. With a capacitive screen, you would need to manipulate a droplet of water or some other conductive material to touch the screen, and with infrared, you would have to manipulate some small object close to the display. (Of the three technologies, infrared is the most sensitive–I’ve had gnats turn pages and look up words in the dictionary on my ebook reader with an IR touchscreen.)
There are also pressure touchscreens, which a TK could certainly use. In fact, they’d probably have an easier time using them than us normies do-- Pressure touchscreens are the nadir of user-unfriendliness.
They can do whatever you say they can do, and there isn’t a so-called “expert” on Earth that has the right to tell you differently.
I dunno - let’s ask MINDQUAD!
Yes, that’s the resistive screens I mentioned.
Depends on how telekinesis works.
Testing them on these different types of screens would probably help to narrow down the physics of the power (if it were real).
Oh man, think of all the dramatic devices! You should get in contact with Noah Hawley!
ETA: Great question btw, kudos to WordMan
If the plot calls for it, yes.
Plumpudding - thanks. It just got me curious to consider. And yes, I hear the folks who are saying “if writer chooses to make their TK work that way” - of course.
I was wondering how this has been explored. A writer may choose to allow the TK powers to have some “haptic” / touch-like qualities. Or maybe the TK has to use their powers on someone physically close to the touch screen in question and force fingers to contact the touch screen. Or maybe a new flavor of TK ends up getting described, where the TK powers extend to being able to manipulate electronics.
Just considering approaches of how that story’s / character’s world would have to work.
I think you are thinking about this too much.
Being a telekinetic in the basic sense of it means you can move objects with your mind. Keyword being “can”. It’s totally voluntary. If you want to move the chair over there with your powers, you focus on the chair and use your power to move it. Being a TK doesn’t mean that you have no control over it or else everything you focus on or look at would be moving all over the place. So … using a touch screen device would be no different than a normal person. You touch it and it functions. You swipe right with your finger and it responds to your touch.
Now to be fair, if a TK tried to use their TK powers to move an icon around on a touch screen, that may be difficult, but why would they? How lazy is this TK person that they can’t use their finger to move something on a screen?
Of course am thinking about this too much! This is the Straight Dope!! 
So, yeah, clearly not a big deal, but given how pervasive touch screens are at this point, it seems like it could end up figuring into a plot or something.
Where it would matter is if the telekinetic character in question is physically impaired. Having established rules as to how telekinesis works(or doesn’t work) will make for a better story.
Can a wizard survive in the atmosphere of Jupiter’s third moon? I don’t know because wizards aren’t real!
Seriously, though, the correct answer is “If the author wants it that way.” *But, *if you’re going to create a world in which telekinesis or other magic exists, you’d damn well better define a coherent set of rules and keep them consistent.
I guess that’s my point: is anyone aware of a storyline where this has factored in? Czarcasm’s scenario of a TK disabled person is one example where figuring this out would matter.
Again, yes, this is not a big deal. Simple a curiosity. Heck, the last time I started one of these question threads, it was to ask how much of Wolverine can be missing to heal back: Wolverine: what's the least amount of him that healed back? - Cafe Society - Straight Dope Message Board
It’s just goofy speculative what if stuff…just not as cool as asking if Superman was so powerful, could he rip his own head off - that was my favorite of these threads 
An interesting variant I thought of once: In the story, the human brain would be capable of telekinesis…but only to do that which the person using it couldn’t already do physically. Flip a light switch on? Only if there was some physical reason you couldn’t reach it(laziness isn’t a good reason).
My first thought for why a teke might want to do this is if they were imprisoned somehow, and the lock for their cell were controlled by a touchscreen device (which of course would be kept out of arm’s reach of the cell, but maybe not out of mind’s reach). Maybe that’s just obvious to me because a recent D&D character of mine was an arcane trickster (for whom using telekinesis to pick a lock is just routine).
How many telekinetics would it take to destroy an M1A1 Abrams?
Points.
The Great and Powerful Turtle could do it all by himself.
Gil “The Arm” Hamilton probably could, too, but via a completely different method.