Sometimes when a bird is trying to get another bird's attention, they'll make a sound that's similar to a baby's begging for food cry. And yes it's annoying, because a baby's cry is supposed to be annoying so the adults will be motivated to make it stop.

Priscilla and Elvis like to butt heads with each other, each one trying to get the other one to preen them, and making the begging cry while they do it. But neither one wants to do any preening, they just want to receive it, so nothing happens.

Is it like this?
https://www.youtube.com/watch?v=bv8uw6JyGw0

you know, something like this actually (but more annoying LOL) !
He just never did it to Cuddles. Didn't need to beg her, I guess

No, that's just an annoying love song. Some tiels are sucky singers.