Hi Earl. This may sound like a silly question but does your bird have a mate that you are positive is a male bird? I say that because lots of folks don't realize that she does not need a mate to lay eggs. She only needs a mate to lay fertile eggs. First off, do not take her egg/s away from her, whether she has a mate or not. There may be more, laid at the rate of one, every other day, up to an average clutch size of 3-5 eggs. If she goes over that, she is getting into deep trouble, health wise. You will have to do everything possible to try to discourage further laying. She needs a place to keep her eggs safe from being damaged but you do not want to provide her with anything that even remotely resembles a true nest box. Nest boxes are semi dark and much too "private and safe". An enclosure like that will only spur her to lay even more eggs than she might otherwise. That's a possible serious health issue which I'll address. I suggest giving her one of the clear plastic, shoe box size storage boxes like you can find at WalMart, KMart, etc. Leave the lid off, line the box with many layers of plain white paper towels, and ever so gently, (while you are probably being pecked and fussed at) move her egg/s into the box. Now, for the health issues. You must be ever vigilant that she is getting enough calcium from a literally bottomless source. The easiest and most obvious is to keep her in cuttlebones. She will likely go through them very quickly right now. She must have very good calcium reserves in order to produce firm, solid egg shells and to help give her body the ability to produce the contractions needed to deliver the egg. If she is calcium deficient, her body will start to pull calcium from her bones. The danger of broken bones is obvious. The added danger is when there is not enough calcium, from anywhere, her eggs will become soft shelled. She will not be able to pass them and will become egg bound. The danger that goes hand in hand with this is an egg could rupture inside of her. Either of those two scenarios is a life threatening emergency and she will die without intervention from a well qualitifed avian vet. If your bird is on a seed only diet, she is in danger of serious health problems, with or without the added physical stress of laying eggs. I'm going to give you a link to diet information for birds. A good quality, name brand seed mix should not be more than 20%-30% of her dailey intake. She needs a good brand of pellets (LaFeber is one of my personal favorites), fresh vegetables, cooked brown rice, well cooked bean mixes, cooked pasta, hard boiled or scrambled eggs, etc. The lists will give you additional suggestions. It will also list some fruits but don't be surprised if she won't eat them. Many Tiels do not care for fruit. If she is on a seed only diet right now, she will probably be resistant to the new, strange items but do not give up. Keep offering them. Just don't leave her "wet" food bowl out more than a couple hours as it can quickly grow harmful bacteria.
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The reason you need to leave all undamaged eggs with her is because Tiels are what we call "opportunistic layers". If her eggs are damaged or removed, she will, more than likely, continue to try to replace them, leading to the above health risks. If something should happen to her eggs so that they have to be pitched, a reasonable substitute needs to be found. You can probably find a reasonably sized facimile egg at craft stores and place them in her box. Beyond insuring she has the safe, yet not private place for her eggs and making sure she has the proper diet and calcium, there is nothing else for you to do beyond waiting her out. Normal gestation time for Tiel eggs is 19-21 days. She may sit her eggs that long, maybe less, maybe more. You just have to be sure, beyond any doubt, that she has totally abandoned them before removing. To take them too soon, is to inspire more. If you have not seen her go near them for at least 3-4 days, then it should be safe to remove them. I hope this helps but if you have further questions, don't hesitate to ask. Patricia.