The mayor said there was no realistic way of tracking the offenders to impose fines for illegal dumping of rubbish.
The compactors were placed before summer and the piles of rubbish were a holiday-time problem which she said was linked in part to the difficulties with freedom camping.
"I would say that it's largely visitors," Goudie said.
"Why is it that we have to keep funding the enforcement of people's behaviour?"
"It's incredibly frustrating. You would have thought when they were coming to an environment like Thames Coromandel District - it's such a beautiful environment - they would have more respect and look after it.
"It's a minority, but a sizable minority, that are disrespecting our environment. It's totally lazy."
"It's the same behaviour we get from some of the freedom campers"
She said the council had provided some freedom camping sites but they had become overloaded and were causing problems.
"Where are they going to the toilet? What are they doing with their rubbish?"
She said the claim of vehicles being self-contained - with an onboard toilet and storage tank - was in many cases "bogus". For some it amounted to no more than carrying a bucket.
The council, outlining its freedom-camping policy, says on its website: "The big rule – you must be in a certified self-contained vehicle if you want to freedom camp. If you're a tourist and don't know if your vehicle complies, ask your rental company."
The council's four roadside rubbish compactors are at Colville, Kuaotunu, Opoutere and Coroglen.