Advice For Property Line Dispute After New Home Purchase

Location: Cook County, Illinois, USA

My partner and closed on a house about a week ago and have been getting quotes to repair the existing fence in our back yard. A few days ago we decided to be good neighbors and introduce ourselves to the neighbors behind our house and ask if they mind that we have contractors passing through their yard to complete repairs or for myself to powerwash and stain the fence facing their property. At this point they inform me that the previous owner (of my house), advised them that the fence is actually on their property and they were planning to cut it down and move it about 12"-18" closer to our house within the next 2-3 weeks.

I asked their reasoning for wanting to do that and their only answer is because they don't want it to be an issue when they go to sell the house and "how would you feel if we had a foot of your property?" They moved in about 18 months ago and never got to it before because they were working on the interior of the house. Once they found out the previous owner of my house was selling, they decided to wait and just deal with it through the new owner (me).

I did advise them that I do not want them to alter or move my fence and that I'd like to see some documentation that they have claim to it.

This raises two issues for me.

One: By moving the fence, we will need to cut down multiple 20+ year old evergreens and it will significantly deteriorate the value and enjoyment of our home.

Two: This property dispute was never disclosed to us and there are permits obtained through FOIA showing this fence was an approved build by the city so we assumed it was a part of our property.

What advice to you all have for me? I don't want to get off on the wrong foot with the neighbor, but I also want to protect the property I thought I was buying.

I've considered adverse possession to ensure that these neighbors and/or future neighbors can't attempt to do this in the future. Not sure how strong my case is. I do have satellite imagery showing that the fence has been there longer than 20 years along with a survey showing it was there in 1979 which I have attached redacted versions of.

Also, do I have any grounds against the seller for failure to disclose the property line dispute? We did purchase "as is".

Are there other options I should consider to avoid extensive/unnecessary costs in trying to fight this?

TL;DR

Bought a house and didn't get a disclosure saying property lines were disputed and now neighbors want to move my fence that has been there over 20 years and damage multiple large trees in my back yard during the process.

Edit adding link to relevant current and historical photos of property along with 1979 and 2024 plat of survey.

https://imgur.com/a/vFtTSaG

Also want to add, that I'm not disputing the property line per se, the surveys show the fence is over the line, but it has been for 20+ years and it was an implied part of the property at time of purchase.