If this is a healthy naturally growing tree, (as opposed to having been planted on the lot line) then I am not so sure you have any obligation to do anything. I haven't done the research to answer in full, but here are some cases that seem helpful.
Ponte v. DaSilva, 388 Mass. 1008 (1983). "The failure of a landowner to prevent the blowing or dropping of leaves, branches, and sap from a healthy tree onto a neighbor's property is not unreasonable and cannot be the basis of a finding of negligence or private nuisance."
Michalson v. Nutting, 275 Mass. 232 (1931). The owner of a tree is not responsible for the damage its roots cause to neighboring property, but the neighbor's "right to cut off the intruding boughs and roots is well recognized."
Macero v. Busconi Corp., Civil No. 99-03577E (Middlesex Super.Ct.), 12 Mass. L. Rep. 521 (2000). "Massachusetts law recognizes a right of self-help by which a property owner can cut the limbs or branches of a tree that invade his property as long as such cutting is done at the property line.
The law evolved during a time when we had much larger properties that could have had over 100 trees that straddled the boundary lines. There was never a requirement that an owner patrol his property to find trees that overhung the lot line. The law was that if an owner was aware of a sick tree that could cause damage if it fell, then the owner had an obligation to act.
My answers are general in nature based upon very short, and often incomplete questions. Please do not rely upon my answers. If you need a legal opinion, you need to hire a lawyer who will take the time to fully understand your problem and then take the time to research the issues.
Your neighbor can hack off any part of the tree hanging/encroaching into her property. Has she give you a reason as to why she does not want to do it herself? If she is old/infirmed or simply does not have the money, then hack it off yourself. From you statement, that you've done that. Bottom line is, if it is something originating from your property and has caused damage or has potential to cause damage, you will likely be liable if she sues you. I don't know what you mean by releasing you for existing damage. You are not in a lawsuit with her, and she is not obligated to sign something. If you think the damage occurred years before, remember, if she sues you, she has to PROVE her case. Anyone can sue anyone, but winning is another story. It is your responsibility to keep your tree from encroaching into her property, so the law does not give you any automatic relief by releasing you from existing damage for taking care of something that is legally your responsibility anyway. You did the right thing by taking care of it, but she is under no legal obligation to release you from any damage. As for her other "demands" I can not comment because you have not stated what they are.
The tree is your responsibility as the owner of property where it is growing, although your neighbor is permitted to cutting any portion of it that infringes on her property. Depending upon when damage occurred, it may or may not be your responsibility. You should consult with a local attorney.
Best wishes to you.
No attorney-client relatonship is created in responding to this question, and advice provided is based solely on very limited facts presented, and therefore may not be correct. You are advised that it is always best to contact a competent and experienced with the practice of law in the county in which you reside, particularly as it relates to family law, child support, custody and visitation (a/k/a "parenting time") issues, including 209A abuse-prevention restraining orders (a/k/a "ROs" in legal-speak), regarding un-emancipated children, under the age of 22.