FYI, there was no umowa o dzielo or any written statements/contracts.
Aside from any legal issues about working without a contract, there's really no way they can prove anything (except perhaps a bank transfer that isn't backed up by any contract for work) and no way some private agency can collect anything from you without going to court, which without documents would be complicated and very costly. If the debt collection agency keep hassling you, ask them to provide written proof (not just their communications with the translation agency) that a debt exists.