The Virgin Atlantic chief is briefly featured in the original 007 film at an airport security scanner, but can only be seen from the back in the edited version.
Shots of the tail fin of a Virgin plane have also been obscured, the sources said.
A spokesman for BA said only that it "previews films before they are screened on our aircraft and regularly edits films" on the grounds of taste and suitability.
The latest 007 film, which shows how Bond acquires his license to kill with its "00" prefix, broke worldwide box office records for a Bond movie, and earned Daniel Craig a Bafta nomination for best actor.
Virgin appeared in the film, according to media reports, because it had helped the film's producers get a plane to Prague where some of the scenes were shot.
Nobody from Virgin Atlantic was immediately available for comment.
Spats between the two carriers go back a long time. Last year, Virgin Atlantic was identified as having provided U.S. and British authorities with information that triggered an investigation of alleged airline price-fixing in passenger fares and fuel surcharges involving British Airways.