There is an adverb specifying place; it is also an expletive. Adverb: Sylvia is lying there unconscious. Expletive: There are two plums left. Their is a possessive pronoun. They're is a contraction of they are. Fred and Jane finally washed their car. They're later than usual today.
If you are using there to tell the reader where, both words have h-e-r-e. Here is also a place.
If you are using their as a possessive pronoun, you are telling the reader what
"they own. Their has h-e-i-r, which also means heir, as in someone who inherits something. Both words have to do with ownership.
They're is a contraction of they are. Sound out they are in the sentence and see if it works. If it does not, it must be one of the previous versions.