Q: What do you say when comforting a grammar nazi?
A: There, their, they're...
The word there has the word here inside it. Most often, it refers to an actual or virtual place. If you can’t substitute the word here, don’t use there.
There’s a light, over at the Frankenstein place.
So how could I dance with another (oooh!)? When I saw her standing there.
To sleep — perchance to dream: ay, there's the rub!
Their has heir in it. So … it refers to possession. Heirs possess things, eventually.
Teach your children well. Their father's hell did slowly go by. (Not somebody else's father! Their father.)
They’re has an apostrophe, which means it is a contraction of two words: they are. Use they’re only when you could substitute the words they are.
They’re not home. (They are not home.)
There is their cottage, they’re not home.
One last point!
If you really aren't sure? Choose there.