You should definately use the past participle. I think the p.p. varies depending on your English background. For example in England the p.p. of "to pet" is "pet". In the United States the p.p. of "to pet" is "petted". Both are correct. Looks like you and your mother each owe one another $20. I THINK.
Guest, Are you British? I have just checked two BrE dictionaries, and "pet" appears as a regular verb in both (meaning that it will add "-ed" to form the past tense and the past participle). Do you know of any written sources where I might find "pet" as a past participle?