Wow, a lot to think about.
To answer some questions: anchors are permanent. I have some, on the opposite side. They were extant when I purchased the property. I think they are on my property, but can’t be sure. Her anchors would be about 6-8 feet from my house. The anchors are done subterraneously, no trench digging (I think). There is no manicured state to return my lawn to, unless we are getting very liberal with the word “manicured”, and somewhat loose with the word “lawn” as well. I just don’t care much as long as it is within code. “Crab grass” is grass too, right? Re-reading his, that makes it sound like I live in a neighborhood one step up from boarded windows. That is not correct, it’s upper middle class I guess - just one guy needs to have the worst lawn on the block, and I volunteered.
I know there are alternate solutions. I’ve seen steel pipe taking some of the weight off the wall by supporting the floor above , for example.
The possible implications on future sales have me concerned. I will practice “soft resistance” (making myself hard to find, ask lots of questions, say “I’m not sure” a lot) until I have that angle sorted out. It’s weird, if this were a business issue I’d have no problems finding 5 ways to tell them to pound salt and have them feel good about the process, but this is somehow different.
Someday you may need to dig in your yard. Maybe you need to install a drain system, or do a repair to your own basement. Whatever the reason, you now have to deal with the practical and legal issues of your neighbor’s wall anchors that are on your property.
Don’t allow that hardware onto your property. There are alternative methods available to your neighbor.
The distance between the neighbor’s house stays constant. Neither neighbor can fix their foundation without intruding on the others property in some way. Driving an excavator over someone’s property is an intrusion and it damages the landscaping. Piling up dirt that sits on a neighbor’s land is an intrusion. Trying to work on homes this close together means some inconvenience and patience.
Cooperating with each other is a necessity. Otherwise neither house gets fixed. The best solution would be to negotiate a discount price with the contractor. He only has to transport his equipment and bring in his laborers one time. Excavate once and do the repairs. Fix both houses at the same time. I don’t know if that is an option being considered or not.
In the OPs shoes I would happily cooperate once papers were signed. However, those legal documents would protect me to the point where the neighbor and her contractor would not be willing to sign.
It’s not an option because the OP’s house doesn’t need fixing, unless the neighbour’s fix breaks it. They have very little to gain and a lot to lose, which is why they are right to be wary.
“I’ve been thinking about installing a geothermal system on that side of the house, and this would prevent it. Not to mention I might need to shore up my own basement walls someday and this would prevent excavation there. I think you’re going to have to figure out a plan that can be done on your own property.”
For what it’s worth, I’ve seen this kind of shoring up done much closer to the wall in question by putting the anchors through big concrete blocks (presumably poured in place) a couple feet from the wall.
You must have a lawyer to protect your property rights, and probably your own engineer. So first step: tell your neighbor she must pay the fees for these professionals or you won’t consider her request. Simple economics: She needs your land, you need professional advice; you need to be compensated for that advice AND for the use of your land. The lawyer should help determine the value of the land use.