Former British Cycling performance director Dave Brailsford told Britain's Culture, Media and Sport committee last week the package, sent to Wiggins during the 2011 Criterium du Dauphine, contained Fluimucil.
But Conservative party politician Damian Collins, who chairs the committee, said British Cycling had not been able to provide a paper trail backing up Brailsford's claims.
"It seems to be difficult to get precise records of exactly what was in this package, why it was ordered and the detail that you would want to know," Collins told BBC Radio 4.
"Dave Brailsford told the committee he'd been told by the team doctor it was this drug called Fluimucil, which is readily available in France, can easily be obtained and there are no restrictions on its usage.
"So if it's as simple as that, why get a British Cycling coach to courier it from Manchester via London to Geneva when you could have just gone to a pharmacy in France and bought it over the counter?
"That's why a lot of people looking at this say it looks odd, it doesn't look quite right."
The delivery has come under the spotlight after it emerged Wiggins, who retired on Wednesday, was granted therapeutic use exemptions for the banned substance triamcinolone prior to three major races.
Wiggins, British Cycling and Team Sky, Wiggins's former team, have denied wrongdoing and there is no suggestion they broke any rules.
Brailsford, boss of Team Sky, told the committee British Cycling coach Simon Cope had brought the package with him to France while he made a scheduled trip.
The Times on Thursday published a receipt showing Cope's return trip had cost £597.65 ($732.39, 699.28 euros).
After travelling to Manchester from southern England to collect the package, he flew to Geneva on June 12, drove to La Toussuire in France and returned to England the same day.
The newspaper said British Cycling president Bob Howden has written to the committee to explain it has been unable to access documents because they are "locked down" by UK Anti-Doping investigators.