Ex Household Cavalryman...I have highlighted the mistake in your post...good effort sit down and rejoin the crew!!
there - (PLACE) - adverb
Put the chair there.
The museum is closed today. We'll go there tomorrow.
There's that book you were looking for.
I'll have to stop you there, we've run out of time.
I've left the boxes over/out/under there.
their - adj. The possessive form of they.
Used as a modifier before a noun: their accomplishments; their home town.
Usage Problem His, her, or its: "It is fatal for anyone who writes to think of their sex"