Review.
Overturn means using legal means to reverse a law.
When a lawyer is using the term "overturn" it does not mean using any illegal means.
Overturn is a commonly used term by politicians [who are commonly lawyers].
Supreme court justices can be involved in overturning some law. Voters can be involved in overturning a law. Etc.
Overturning a law passed by voters, means one will follow some legal process.
And by definition of the word "overturn" as used by law it will involve the courts or legislative act

Seeking to overturn a law passed by voters means one looking at the legal options which could be available. Which generally means one is having a lawyer or lawyers examine the merits involved in that possibility.
It is possible, that you could *even* be highly in favor a law on term limits, and still seek to overturn a law on term limits. E.g. for law to be considered firm/strong attempts to challenge it, is normally seen indications of it's strength- conversely something on the books but which has never been enforced or legal challenged is generally considered "weak" and therefore perhaps not very binding.
And it is possible, that after reviewing the legal options, that no legal action is taken. Though seeking to overturn a law could also involve more than simply looking at a bunch of law books and/or getting legal opinion- it could involve filing preliminary proceedings or whatever.

I hope I have established that by seeking to overturn some law, this does not by itself in any way suggest some "subverting of democracy".
I'm not "trying to argue this fact". It's too elementary to be worth an argument. Considering the obvious that our democracy keystone principle is rule by law. It's about the same as arguing abut whether the act of citizens voting "subverts democracy".

Ok. So what else is causing you a problem?
That Rudy is talking some elected officals as in "Rudy attempted to modify it by agreement between the sitting mayor and the mayor elect".
Let's make something very clear, if either the sitting mayor or the mayor elect did not want to talk to Rudy, Rudy would not be able to talk to them. Legally, they could prevent any discussion with Rudy, just if they can prevent any discussion with any bum on the street. So, as far as this discussion goes, we can assume they wish to discuss some matters with Rudy. And discussing matters with elected representatives of the people is not in any way "subverting of democracy" but rather is an essential part of our democracy.
And assuming that Rudy actually wants to change an agreement between sitting mayor and the mayor elect, we can assume that Rudy won't be using a gun to have them change their minds, but rather they might make this decision after a conversation/argument makes them thinks that it would be a good idea to do so.