“There’s still an outstanding balance...”

Solution 1:

The following comment by @TrevorD provides a suitable answer:

Your first sentence is perfectly fine. My only minor quibble would be that, in writing, I would not abbreviate "There is" to "There's". In option 3, "outstanding unpaid" is tautological - either word will do, but not both. I may omit "to be paid" from the first sentence.

Your second option is also fine, but I think (at least in the UK), "outstanding balance" would be the more usual expression. (If there is any doubt whether it is a debit or credit balance, the inclusion of "unpaid" would make that clear - but it would normally be clear from context (else you wouldn't be chasing them!)).