It is very difficult to know exactly what this is without seeing it, but it sounds like on of two things – both of which are some of the most common ailments in caged birds. Firstly, budgies are prone to Cnemodocoptes mites. These can cause a scaly build-up on the surface of the beak, and often the feet too. This often looks like a lump of hard scales with many tiny holes in it, and unfortunately it often goes unnoticed. If you visit your pet store or vet, they should be able to supply a suitable medication for your bird.

Alternatively, your bird may simply have a wart, which is caused when papillomavirus infects skin cells. In budgies, the most common site of wart growth is indeed on the beak. The virus responsible for warts in birds has not been identified as transferable to humans. As long as the growth does no affect breathing or give discomfort, there is not a lot of treatment available. The wart can either be surgically removed if necessary or chemically removed. Only if the wart continues to grow or many more are found, should you be concerned that this growth could be a tumor.