I will assume when the OP said the TA made reses for my family, that the OP themselves was traveling or at least that every passenger had the same last name as the OP. if true then whats the difference who made the booking? if however the OP wasnt flying and those who were didnt have the same last name or live at the address on the OPs profile, the OP is pretty much toast.

now if say the tkts were for his married daughter and her family(didnt last name) the OP is gonna have to prove beyond a doubt thats its his daughter

anything beyond the above tells BA the Avios were sold which is a nono

personally I dont get why anyone would pay anyone to book them a trip using their own miles. now if the OP bought the Avios from the TA who somehow got them transferred into the OPs account that too would be a nono and goodbye Charlie