05-21-2016, 02:10 PM
Welcome to the forums.
From the photos, I'm unable to take a good look at the beak.
Since your budgie is tame and you are able to have him/her on your finger, you should be able to get a much better look and see if that is the left over of a veggie or fruit treat that got stuck on the beak.
The feathers around the beak and above the cere area also seem somewhat unkempt. The lighting on the photos really isn't the best and I can't tell if the feathers are truly soiled or if your budgie is actively moulting or not.
Besides that, have you noticed a change on your budgie's droppings, a decrease on activity levels and appetite?
You do well in having your budgie properly examined by an avian vet specialist.
Best of luck with everything, I hope your budgie's condition improves soon.
RIP sweet Tito (Summer 2008 - January 17th 2013).
You are missed and never will be forgotten.