According to the CMA, some Teletext customers said they were promised refunds by a certain date, only for this date to be pushed back.
The watchdog said on Thursday (4 February) it would engage Teletext to gather further evidence and establish whether the company has broken consumer protection law.
"We understand that the pandemic is presenting challenges for travel businesses, but it is important that the interests of consumers are properly protected and that businesses comply with the law," said CMA chief executive Andrea Coscelli.
"We’ll be engaging with Teletext to establish whether the law has been broken and will take further action if necessary."