Bill sent to Collections WITHOUT a signed contract?

Background: over a year after a house cleaning service did an inadequate/incomplete job and I offered to pay their FIRST estimate that they gave (they later raised the price WITHOUT authorization), I receive a letter from a collection agency for the amount PLUS interest. I never signed ANY paper for the work, and when I told them I would pay them the first estimate they said dont bother, that they would just take me to court for the entire amount anyways. A year later, thinking they realized they were in the wrong, I get this letter. If I notify the collection agency and tell them there is no contract and the job was not performed as agreed and the price was NOT agreed upon, will I be off the hook? Can they legally do anything without the contract that doesnt exist?