Wiggins and Team Sky principal Sir Dave Brailsford insist triamcinolone was medically necessary for a pollen allergy that aggravates his asthma and the TUEs were approved by cycling's UCI world governing body.
Questions have also been raised over a package delivered to Wiggins and Team Sky at the end of the 2011 Criterium du Dauphine, a race won by Wiggins.
The contents of the package have been the subject of a UK Anti-Doping investigation into alleged "wrongdoing".
Last week, Brailsford told a Department of Culture, Media and Sport select committee that the package contained fluimucil, an over-the-counter decongestant available relatively cheaply in France.
But that doesn't explain why the team went to such expense to have the package personally delivered to Wiggins by British Cycling coach Simon Cope.
All parties deny wrongdoing.
Select committe chairman Damian Collins MP said in Thursday's edition of "The Times" that British Cycling evidence failed to confirm Brailsford's explanation.
"The more we discover about the package, the more questions seem to be thrown up," Collins said. "We now know from Simon Cope's expense claims that the request to take the package must have been made some time in advance and that he travelled from southern England up to Manchester to collect it, and then went back to fly to France from London Gatwick.
"If this medicine was needed urgently, it would have been much quicker to buy it in France. We also know from last week's hearing that the medication was administered as soon as it was delivered.
"It also seems that British Cycling do not know, categorically, what was in the package. They say they understand it to be Fluimucil, but do not explain why they understand that's what it was.
"We need to be sure that British Cycling do keep proper records of what goes in and out of their medical stores."
Earlier this year, Wiggins, who conquered his sport on the road, as well as in the velodrome, won his fifth Olympic gold in Rio as part of the world record-breaking pursuit team, adding to a tally that also includes a silver and two bronzes.
He competed in five successive Games from Sydney 2000 and reached a career high in 2012, when he completed an unprecedented double of a maiden Tour de France victory with Team Sky and a home Olympic triumph in the time trial in London.
"I have been lucky enough to live a dream, and fulfil my childhood aspiration of making a living and a career out of the sport I fell in love with at the age of 12.
"I've met my idols and ridden with and alongside the best for 20 years," Wiggins' retirement message read.
