I'm sorry your budgie is so bothered by that particular tail feather.
Despite the moult, by looking at the photos it seems her general feather condition isn't the best. I can see it by looking at overall plumage and at her scruffy tail and flight feathers. She also seems to be somewhat overweight and due to this she may not be able to properly preen an tend to her feathers.
Have her feathers always been like this? Give your budgie's current condition, it would be best to book her an appointment with the avian vet for a full check-up.
I couldn't help to notice the sandpaper covers on the perches. In order to prevent your budgie from having sores or from possibly ingesting the material by chewing at it an getting sick in the process, it's best to remove these from the cage.
There are much better alternatives to keep the toenails and beak well maintained by having wooden perches of different sizes and diameters, a pedi perch or mineral/calcium perch will also help in filing the toenails.
Best of luck with your budgie girl, I hope she feels better soon.