More than 12,000 have signed a petition calling on Birmingham City Council to refund residents a proportion of their Council Tax for each missed bin collection.
Industrial action resumed on Friday after the Council issued redundancy letters to 106 refuse collectors.
The petition was set up by Birmingham City Councillor Alex Yip. It reads:
On the council's website, it says that Council Tax is not paid to fund a particular service and there is a legal obligation to pay it.
On Saturday, the arbitration service Acas took the unusual step of clarifying its position in the war of words between Birmingham City Council and the union representing the city's striking bin men.
Their union, Unite, said the Council was going back on an agreement reached at Acas to protect all of the workers jobs.
The Council Leader said he never made any such agreement.
In a statement Acas said:
In response to this, a Birmingham City Council spokesperson said: