The Channel Islands regulator (CICRA) found satisfaction with JT's mobile services had fallen.
Tamara O'Brien, from JT, said the survey results "directly contradict" its own commercial data.
In contrast, the other two operators in Guernsey and Jersey, Sure and Airtel, saw a rise for both areas.
The survey questioned 500 islanders in each island November, after the first was carried out in May.
It also looked at whether customers had or were likely to change providers and how happy with customer services those who had contacted them were.
On Airtel, those who rated the quality of service as "satisfactory or highly satisfactory" rose in Guernsey from 82% to 88% and in Jersey from 67% to 78%.
Sure customer satisfaction rose from 59% to 70% in Guernsey, but fell in Jersey from 90% to 78%.
For JT customers it fell to 40% in both islands, from 49% in Guernsey and 55% in Jersey.
CICRA director Louise Read, said: "I would urge JT to listen and react quickly and decisively to the feedback from its customers."
But, Ms O'Brien said the firm listened carefully to customer's feedback but believed "a note of caution" was necessary.
"Having analysed this most recent survey by our regulator, we think the conclusions drawn by CICRA need further scrutiny," she said.
"Our customer satisfaction surveys, conducted every quarter by independent market research professionals, show a very different picture."
Ms Read said: "We want operators to use these surveys to raise the bar so they're delivering increasing levels of customer satisfaction.
"We will be sharing all the methodology and all the results with both JT and all the operators."
Ian Campbell, chief executive of Airtel-Vodafone, said he was "delighted at the outcome" after his company rated highest in most categories.
A Sure spokeswoman said it was "still working hard to make our service even better".
Results of a survey that found falling customer satisfaction in a Channel Islands firm's phone services have been disputed by the company.