Hi Edie,
Finches only need a nest for breeding. They should not have a nest year round. Wild birds do not sleep in nests. Leaving the nest in the cage all the time can cause issues. Either it can make them breed and lay eggs over and over – which is very bad for the hen – or what is likely in your case, he may want to breed and nest and she isn’t in breeding condition. I would remove the nest, and wait until you see them mating and showing signs of wanting to nest. Both birds need to be at least a year old – 18 months is better. If they are younger than this, then that is the main issue because they are too young to breed, and should not have a nest in the cage at all. If you don’t want them to breed at all, then do not give them a nest. You should have one perch that is high in the cage, and that is most likely where they will want to sleep.
Thank you for asking Lafeber,
Brenda