How to properly break a Contingency Agreement

We had signed an Insurance Contingency Agreement with a roofing company. They did a horrible job with our tarping and now want to overinflate the roofing cost to meet the insurance payment. We told them we no longer want to use them for the roof replacement. They threatened to contact their attorney and the insurance company. Since this happened we received a Claim of Lien from them regarding payment for the roof tarping they completed. I have no issue paying this since the work was completed (even though it was not a good job and we got a lot of water damage as a result). We want to make sure we follow the correct steps to remove the lien and pay the balance due. We also want to make sure we put ourselves in a good position to prepare for them coming after us regarding the Contingency Agreement we had signed after the hurricane hit.