How many eggs do zebra finches lay and how often?

Nooo! Lol, dont take the eggs out. How many birds do you have and do you know their es? If you have a male and female and you don't want babies then you can boil the eggs and replace them in the cage or otherwise you can buy false eggs to replace the ones that she layed. When they don't hatch the female will give up on them and then and only then can you get rid of them. If you remove them straight away she will continue laying until she gets a full clutch of eggs, which is 3 - 8 eggs and this will damage her health badly. She will eventually get bored of laying eggs and wont lay anymore. Good Luck!