They were late again, (much) 'to our annoyance'. [=it annoyed us that they were late again]
She shook her head 'in annoyance'. [=in a way that showed she was annoyed]
The long wait at the restaurant was a minor 'annoyance'. [='nuisance']
(..) to pick up the letters. That'll give you the grounds to make the arrest. You get him, and we get away. To the Germans, that last will be just a minor annoyance. There's still something I don't understand. Miss Lund, she is very beautiful, yes... ...but you were never interested (..)1942 Casablanca