We had roofer that came and was not doing a good job, we ask how everything was going to be fixed to make it right. He stated that he was going to wash his hands of it, take it as a loss and told us we would not owe a dime. He then signed a document and wrote “paid in full”. Now he is demanding payment and threatening to place a lien on our property.
Sorry to hear about the issues you have been having. If the contractor wrote "paid in full" on a check or document, the document or check is often legally binding. A contractor has mechanics lien rights by law by improving a particular project. If the contractor has not been paid for their work even if their workmanship is in dispute , it is very difficult to prove that their mechanics lien is invalid.
However, if the contractor was issued a check that stated "paid in full" and the contractor endorses said document or check then the GC has no contract rights and loses their lien rights. Considering the GC in your case endorsed the document in which he specified "paid in full", it is likely he has no lien rights.