A collection agency has threatened to put a lean on my home if I don't pay the $3,800 that they claim I owe. The original balance of the debt was $1,000. Is there a way I can get out of paying the larger amount and avoid going to court?

You could try to negotiate with them. Offer to pay them a $1500 settlement.

That is, assuming that you do in fact owe them the original 1,000