Dear Heloise: I have been drinking hot black tea at work from an insulated plastic tumbler with lid (something like this but not exactly) and not surprisingly it is now stained from the tea. Searching online reveals three preferred methods for cleaning. Please share your expertise and experience. Please don’t recommend another drinking cup, I like this one because it’s bigger than any of the metal ones.
If it makes any difference, the plastic is clear.
Warm water, with or without dish soap, and a bit of bleach, like a spoonful. Soak. Rinse well.
I’ve found a good brush or scouring pad with a little soapy water works wonders. Given the shape of the tumbler, the brush would be better.
Magic erasers - any brand will do - grocery stores have them. Dampen the sponge - wipe the cup - rinse the cup - use the cup - repeat as needed.
Commercial pot cleaners like “Clean That Pot” or “Squeak-n-Clean” can work small miracles as they have the chemistry to handle the oils and tannins that make up the stain.
Ooh, I already have one of those!
Why do the stains need to be eradicated? It’s just tannins. Not dirty or unhygienic.
I did vote bleach or other commercial cleaner, though.
A magic eraser is basically very fine sandpaper. That might scratch the plastic tumbler more than the OP wants.
Yeah, this. I’m a big tea drinker and one of my favorite cups is clear plastic. I wouldn’t use a scouring pad lest it scratched the surface.
However, you can also tell people what my husband does when they comment on his badly stained coffee cup: Its great, and if I run out of coffee all I have to do is fill it with hot water and scrape the sides…INSTANT COFFEE! 
I checked bleach, etc., but I have found that Soft Scrub With Bleach is great for this kind of thing. It has a mild abrasive that won’t scratch hard surfaces, although I’m not sure about plastic.
toothpaste
denture tablets