Since this pair isn’t bonded, and you know the eggs are not fertile, the best thing to do is take down the nest box and just put the eggs on the cage floor. By letting her have the box, you are actually encouraging egg laying, and female cockatiels are notorious for becoming chronic egg layers in captivity If this happens, you often need to take her to a Vet for hormone treatment to keep her from laying so many eggs that it kills her. Most likely, if you take down the box and move the eggs, she will abandon them. Then you can focus on making some changes to discourage more egg laying. As I said before, I think if this pair eve did bond, you would regret giving them up as pets, but I feel like they are too bonded to you for them to bond with each other unless you cut them off from your attention entirely.
You need to do all of these things to discourage egg laying. Keep in mind that to lay eggs, she needs longer daylight, warmer weather, abundant food, and a quiet, private environment. Your goal is to reverse these conditions.
Limit her light to 8-10 hours by covering the cage early each evening
Do not give her anything to use as a nest – no bird huts or tents, no box, bowl, etc. If she decides to sit in a food bowl, remove it and replace with smaller cups.
Do not give her anything to shred such as paper or cardboard.
Rearrange the toys in the cage frequently.
Move the cage to a different place in the room. Move the cage about once a week, or whenever she shows signs of nesting – settling on the cage floor for example. This disrupts her idea of having a stable place to lay eggs and raise chicks.
If you feed a lot of fresh foods, stop offering any for a couple of weeks, and then only offer them in small amounts about 2 or 3 times a week. You can resume normal feeding later when the birds aren’t being hormonal.
If she is let out of the cage, do not let her get in any dark cozy places and don’t give her free roam.
When you handle her, limit any petting to her head and neck – do not pet her on the body. Only a bonded mate is allowed to groom the body. We can’t be a mate, so touching the body is off limits.
If there is no metal floor grate, then do not use any bedding or paper in the cage tray – leave it bare and clean it daily.
All of the above can apply to the pair, not just the hen.
Thanks for the update,