The best thing to do is remove that food tray and replace it with a few smaller cups that they can’t fit inside of. Spread the food cups out so none of the finches can claim all of the food. Basically these guys are exhibiting nesting and territorial behavior, so any time they try to nest in something, it needs to be removed. Finches can do well in groups as long as you have an even amount of birds and do not give them nests. Once breeding gets into the picture, you are dealing with territorial birds and this will eventually turn into serious fighting. As you have found, even with same sex birds, nesting behavior can pop up, so to avoid it, remove anything they try to claim as a nest. Moving the cage to another place in the room every once in a while can help, too.
Thank you for asking Lafeber,