Hello there, welcome to the Forums to you and Storm!
Although I have no particular experience with eclectus parrots, I am the mother of a chronic little egg-laying lorikeet called Lilly, who will lay infertile eggs anywhere and everywhere given half a chance! Chronic egg-laying like this can cause your hen to become depleted in calcium in her bones and other various nutrients if it continues, or could even result in egg-binding so you do want to take steps to stop it.
If and when my Lilly starts to lay eggs (which I do everything I possibly can to prevent but sometimes she just has a mind of her own!) I boil the eggs, let them cool, and return them to her to sit on. This prevents her from continually laying more and more and allows her to work off her maternal yearnings until she loses interest of her own accord, which usually takes about a month. Boiling the eggs when they're infertile will assist in the event that your hen breaks the eggshell during a determined stretch of sitting, which could leave you will a nasty smelly bacteria-laden mess to have to clean up, and to clean off your bird which I'm sure is something you'd rather avoid! You can also buy plastic or ceramic dummy eggs that are made to be the correct size for almost any species. As nearly as I can tell, eclectus lay a clutch of only two eggs and incubate them for around 28 days, so give your hen two either boiled or dummy eggs to sit on until she realises nothing is hatching and she should lose interest in them all by herself.
Once this cycle of laying is over, it is important to remove ANYTHING remotely resembling a nest and prevent access to any nesting material either inside or outside the cage. My Lilly has never had a nest as such but she LOVES to burrow behind the cushions on my couch, so if she even looks sideways at them I strip them all off so that she has no access.
I wish you the best of luck with your hen. If the egg laying persists beyond even this, I would strongly suggest you consult your avian vet, because chronic egg laying can be a very worrying condition and I am glad you are here and seeking help
