I have done this in the past on siding and it worked very well, it's worth a try: Mix up a batch of warm water and white vinegar, the mix is 50/50 [On brick or stone, unpainted, I use the vinegar full strength]. Take an old rag and soak it in the water/vinegar solution. Lay it over the egg splatter and hold it in place with a 1x2 or pole for about 15 to 20 minutes. This will get the bulk of it off. Next you need some laundry detergent that contains a protein enzyme. Make sure it has this enzyme or it won't work. Mix the detergent with warm water to form a sticky paste, apply this paste to the remaining egg stain and all those other little splatter spots around and below it. Often their is a long streak running down the wall from the egg. As soon as the surface of the paste starts to dry, wash it off with a scrub brush and warm water.

I am thankful to come upon this site since our pool installer made us feel like this is something they never see and do not want to take any accountability. They told us we need to hire a power washing company. We live in SW Florida and recently had a pool installed and chose Silver Travertine for our decking. We do know travertine is high maintenance but was never warned about the staining that would occur immediately after install. It looks awful and the fact that this was a huge upgrade in our pool build we are regretting going with it. After just a few weeks after install on our covered lanai all of the rust stains and white powder started appearing. Also all of the silver travertine around the pool area in the sun always feels like it has a chalky powder residue on top of it and never feels clean. We paid extra to have cement poured first under the pavers. On top of the cement they put a sand base down before laying the travertine. They claim that this is the proper install. Here are photos of the stone under the covered lanai vs. in the sun around the pool.

I’m going to agree with Joseph on this one. You basically have two choices but both will require you to replace the screws. (Depending in the size of the screw that’s in there go with a stainless #8x2.5” trim head). I’d start by backing out a couple screws and hitting it with a sander to test how deep the staining goes. If it’s surface then you can replace the screws without flipping the boards and just give it a good sanding. Option 2) If staining is deep you can try flipping the board hoping there’s no staining on the underside and face screw the boards back down. Option 3) and one I would’ve recommended from the get go... Use a biscuit joiner like Joseph showed in the video and cut a slot in the side of the board while utilizing a product like the Eb-ty Precision Clips for Ipe which I believe are the best product in the hidden fastener market. Unfortunately though, if you go the hidden fastener route, now you’ll be looking at empty screw holes on the face of your boards. Whichever route you go, while certainly a bit of a hassle, the issue is pretty readily rectifiable. Part of the beauty of wood over composite decking. Worst case scenario sanding should solve the problem and you’re deck will look like brand new...

Were this mine, I'd consider building a dual purpose feature (fire pit/BBQ) since your foundation is already there. Choose the height of your raised fire brick burn pit carefully and, from the higher deck, it could be a fire pit but while you're standing on the lower deck, the added height would make it usable as a BBQ. You would, of course, need to remove the railings from around it. Edit: Or not. On a windy day, that could be dangerous.