I'm not sure why this is a concern, but inter species horizontal gene transfer (in insects) isn't really something that happens. In bacteria sure, in plants maybe, but this is very much not a case of, "Eat a mosquito, get a gene".
Therefore, there's nothing of consequence to transfer to another species. You'd be transfering a gene that doesn't do anything.
Even if, in addition to transferring to another species, it somehow replaced the working gene in some individual, then the gene would simply die out due to the heavy selection pressure against it, leaving the rest of the population unharmed. (To counteract that with the mosquitoes, I take it fresh supplies of the engineered males are going to be repeatedly introduced?)
Eating, no.
But it's my understanding that while uncommon, it does happen that viruses transmit genes from host organisms. Since the virus is hijacking the host cell's reproductive equipment, and all that DNA is just hanging around there, it's easy for some host DNA to get incorporated into the next generation of virus.
(Conversely, I believe that one theory for the origin of "junk" DNA in our genome is that it's viral genetic material accidentally incorporated into the host genome.)