it depends on which paint you are using, and which thinner for that paint
For most paints and thinner combinations, you don't want to do that at all. You also don't want to pour thinned paint back in with your fresh paint.
For some acrylics, you can thin them with the company thinner and pour them back in or store them just fine. I know, 47 people will now say "Never do that!!" , but, they don't use those brands, or they would know that the tip to getting them to last a long time is to replenish the amount you took out of the bottle with the "house brand thinner" or distilled water after each usage. (so, "don't pour water thinned paint back" but, it is suggested to "add water to your paint for long life", lol)
So, for Model Master, Polly Scale and Aeromaster,,,,it would be okay, MisterKit and LifeColor also,,,,,,but, not any acrylic that you thinned for airbrushing with Lacquer Thinner. I also think that the Vallejo group of paints doesn't like it, but, I am not sure, I don't use very much of those.
Back in the day the "don't pour thinned paint back in" became the Meme, partly because we could thin Testors and Pactra PLAs with Ronson lighter fluid, and it turned into goop practically overnight in the jar.
I have 3 year old bottles of Aeromaster that have been thinned and shaken from the beginning,,,,,,and they are still liquid in the bottle. (3 years old at my house,,,,,plus they had to be 10+ years old when I bought them) And they don't have any flakes of dried paint in them, either. (the other acrylic Meme)
I would say get a spare bottle and experiment a bit,,,,,,,,,and then you will know for sure, with the exact liquids you are actually using.
Rex