My tiels' behavior about scritches puzzles me. Typically, Emma bows her head under Silver's. He obligingly starts preening her head. She accepts a couple of seconds of preening, then bops him with her beak. He backs off. Then, she bows her head again.

Silver begs scritches from me. After a few seconds, he bops me with his beak.

The only time Silver wants extended scritching is when he is perched on my forefinger and I am scritching him with the thumb on the same hand.

Why do they ask for scritches, then seem to reject them, then ask again?

For some reason they want it to stop temporarily, and if you think about what was going on just before the bop you might be able to figure out what that reason is. But they don't want it to stop for very long.