I don’t believe that T3 ever intended, nor were required to, paint there aircraft in full BE colours. The quote below is taken from this press release that was issued when BE & T3’s partnership was first announced.
EASTERN AIRWAYS AND FLYBE TO FORM AN ALLIANCE Eastern Airways
As part of the franchise partnership, Eastern Airways routes will operate with Flybe’s BE flight codes. Eastern Airways livery will be retained on its aircraft for scheduled services and the carrier’s ad-hoc charter services and corporate shuttle operations.
I think the small Flybe stickers applied to some Eastern aircraft will be all the Flybe branding that the rest of the fleet are likely to receive.