One process for suppressing a gene is called "DNA methylation". There may well be others, e.g. a demiurge from the quantum processor in each cell ~ something like that ~ we just don't know yet.
No change in the genome is required for birds to NOT express teeth, nor is a change in the genome required for birds to express teeth.
Mammals somehow suppress the growth of extra tooth sets ~ reptiles have no such problem. Neither do birds. There's work afoot to determine how we can remove the suppression ~ and thereby eliminate dentistry.
All well and good. But why does that happen in modern birds when it didn't happen in ancient birds?