They said the facility, which is offering spaces for six caravans, was too small when the average encampment involved groups with 10 or more vans.
Opponents also raised concerns about impact on traffic, services in the area and a lack of consultation with residents before the decision was taken.
Labour ward councillors and MP Valerie Vaz accused the ruling Conservative administration of making a political decision by putting it in Pleck rather than elsewhere in the borough.
Council leader Mike Bird refuted claims it was a political decision and said Pleck was the only suitable site the authority owned for fulfilling the legal obligation to provide a facility.
He also said any issues around the site would be picked up during the consultation process.
During a scrutiny committee meeting to discuss the issue last month, traveller Abiline McShane said the GRT community felt they were not wanted anywhere.
Critics of the objectors have also argued there would be no opposition to the site being used for housing instead of a facility for travellers.
But Pleck councillor Naheed Gultasib, who handed the petition in, stressed the community was not prejudiced against travellers and their concerns were solely about the suitability of the site.
She said an incursion on the nearby Morrison’s car park in March saw 10 vans pitch up.
Councillor Gultasib said: “The petition has been used to give the impression we are racist and that we don’t want the GRT community there.
“That is not the case. It is a site not fit for purpose for the GRT community based on the facts of the numbers of UEs we have coming here.
“There will be six spaces for a caravan on this facility and many UEs in the borough have featured 15 or more.
“People are not concerned about it being the GRT community and they are not saying there isn’t a need for a transit site in Walsall.
“But the fact the site can only take six caravans. If a large group arrives, where will the rest go?
“One of the accusations levelled at us is we wouldn’t have an issue if it was a housing development but we have previously opposed developments, such as the housing scheme at the Harvestime bakery site in Birchills, which we felt was unsuitable.
“The councillors are representing the residents who feel they have been ignored and are now being made to feel as if they are the guilty ones even though this was put on them.
“I think the GRT community is being sold a dream that doesn’t exist. People are rushing to get a facility they are not looking at what the GRT community actually needs.”
With the petition bearing more than 1,500 names, it could spark a debate and the next available full council meeting.
It is currently being considered by planning officers and will be discussed at a committee meeting in the coming months.
*Councillor Naheed Gultasib is defending her seat in this year's local election, with Jitu Miah also standing for the Conservative party.