It's hard to tell (online) what this is, but some of the more usual culprits are infection of the uropygial gland, papilloma or pox. They all sound pretty scary, but your human residents are not at risk, especially when basic hygiene is followed after handling a bird or cleaning a cage.
Uropygial Gland problems are also not uncommon as the result of vitamin A deficiency (largely seed diets). This gland is also called the preening gland or oil gland. It’s located at the base of the lower back where the tailfeathers start.
When you watch your bird preen, they will go to this area and then drag their beaks through the rest of their feathers. What they’re doing is picking up necessary oils from the gland and distributing it throughout the feathers. You won’t ‘see’ the oil, but one of its functions is to keep these beautiful feathers waterproof.
All birds are waterproof to some degree. Some, obviously more than others (like ducks). Cockatiels and other smaller birds tend to be much less waterproof and very soon after hitting the water become soaked and begin to sink. Another benefit of the oils from this gland is to act as an antibacterial, inhibiting the growth of various bacteria that may degrade the feathers.
Amazons and the biggest of macaws (Hyacinths) are among the very few species of birds that do not have a Uropygial Gland.
Sometimes this gland will become infected or impacted. Using very warm water to soak the area while gently massaging it, you may loosen any crusting or minor blockage that could be causing your bird some discomfort and make the area seem swollen or their feathers looking dull and unkempt.
Another possibility is a "wart". These are actually papillomas and can occur on any bird in a variety of locations, including internally.
Papillomas do have the potential to hurt. Your bird will, by nature, hide any signs of pain, so please don’t wait until it’s so bad you can’t miss it because they can’t hide it anymore.
The only treatment for papillomas so far is removal, usually cauterization, as they appear. By maintaining this treatment many birds find many more years left of a good, quality life save for the times this surgery is necessary.
If an attempt to clean the Uropygial gland doesn’t resolve the situation or if the problem recurs, you need a vet to figure out what’s really going on and only a hands on visit can do that.
I hope everything is fine for this lucky bird with the responsibility and honor of keeping some very special individuals happy company.