I just lost a budgie that had a tumour near her anus – it was actually two different tumours. It grew very quickly over the course of a couple of months.
I took her to see three different vets – four different times. The location of the tumour made it difficult for it to be removed without doing damage to her anus area. She was 9.5 years old at the time and surgery would also have been too dangerous. She lived with the tumour for two months and was her normal active self until a day or two before she passed away.
Because he is picking at it, I recommend that you take him/her to an avian vet asap to see if anything can be done. He will need antibiotics at minimum to prevent infection. How old is he/she? Is he acting normally otherwise?