You need to ask them what clause in the contract do they think means that a quote assessed and implemented late now means it can revisited. They wont be able to find one.
Their only remedy if the PM is late in assessing is for the Contractor to notify (in writing) of the lack of response which if ignored for another two weeks would lead to a deemed acceptance. They did not (seemingly) do this so it just means it would never just be deemed accepted. It sounds as though the PM has gone on to assess and implement by confirming in writing their assessment, all be it later than the contract stated.
The Contractor can go to adjudication if they think the assessment is contractually wrong - but the fact it was assessed late itself makes no difference.
Their only remedy if the PM is late in assessing is for the Contractor to notify (in writing) of the lack of response which if ignored for another two weeks would lead to a deemed acceptance. They did not (seemingly) do this so it just means it would never just be deemed accepted. It sounds as though the PM has gone on to assess and implement by confirming in writing their assessment, all be it later than the contract stated.
The Contractor can go to adjudication if they think the assessment is contractually wrong - but the fact it was assessed late itself makes no difference.