From the "mother" of one naughty little egg-laying minx to another - congratulations! I think!! Unfortunately however, where there's one egg there's often another already forming so don't be surprised if another emerges in the next couple of days. Not always the case, and if you're lucky this may be a once-off event, but it's fairly likely.
Exactly how you deal with this will depend a lot on how much interest Ellie shows in her egg/s. I'm certainly no authority on Greys, but many species show little or no interest in the first egg or so until they have laid the entire clutch, which can be between 2 and 5 eggs according to what I read on the interweb. If she shows absolutely zero interest in them even after having laid more - TERRIFIC!! It might even be a good idea for you to boil the egg that she's already laid now that it's out. Even if infertile, boiling the egg gives it a bit more durability in the event that she does want to sit on it and work off those maternal yearnings until she loses interest of her own accord. If she does want to sit and ends up breaking the shell, having boiled the egg means you won't have a nasty, smelly, bacteria laden mess to clean up! Lots of people, myself included, keep dummy eggs on standby just in case their hens start laying again - taking away the eggs prematurely before the hen loses interest in them herself often only leads her to go and lay more. You can get some pretty good faux eggs from the company linked up below...
DummyEggs sells 8 sizes of plastic broody bird eggs to Stop Egg Laying fast, safely, naturally. Non-toxic, fake bird eggs made in USA.
www.dummyeggs.com
In terms of how to stop it from happening again, well I will tell you what I have to do with my Lilly. NO petting or scratching anywhere other than her head or neck, zero access to anything that might even remotely resemble a nesting site - tricky with a tiny purple crowned lorikeet let me tell you! I have to strip all cushions, throw blankets, etc etc off my couch every day and keep her from burrowing into any nook or cranny she may find around the house - again pretty tricky with such a tiny bird! Her peak breeding season runs approximately 6 months of the year but purple crowns are opportunistic breeders too so this means it is a daily regime - again I am not an authority on Greys so unsure if you will need to be so strict on a daily basis.
I hope some other members more experienced with Greys will share their experiences with you soon. If there is good news to be had out of this situation, it would be that Ellie is obviously pretty happy in her new home with you, because unhappy parrots don't tend to lay eggs!