Can someone tell me if the following sentence is correct
as it pertains to the use of the word [there]? thanks

"We are trying to make this a private party event so your
RSVP would be appreciated. Last time we went Paint Balling
we were put up against an ROTC team that had there own guns
and camouflage outfits."

Jake, you want "their".

There is a useful section about they're, their and there here. Good luck at the paintballing.

Thanks Craig

Definitely 'their.
And you really don't need to include 'event'as it is superfluous.