Lee Carré
“the note is very unspecific. There are tons of cottages in Jersey”

While it doesn't spell out precisely how to map, it's an indicator of something missing which is in demand by someone, enough that they bothered to make a note.

It specifies the type of dwelling, which is seldom apparent from imagery.

It also gives the area of concern, rather than all cottages on the island.

A brief look at imagery of the area shows several unmapped buildings.

“the note is located in the middle of the road”

I would suspect that this was by an inexperienced mapper, using their phone, and didn't realise that by default the note is positioned where the phone is, and should be moved. There is also a documented StreetComplete bug which caused notes to be displaced from their intended position.

“it's made by anonymus, without a chance to communicate”

This is a by-design intended feature of notes, else an account becomes a barrier to entry.

“the note was two years old when I closed it”

So? I've opened notes which are considerably older.
A note should be closed when it's resolved, not merely old. Age suggests that it should receive attention over newer notes. Not all notes are of equal complexity to solve.

The goal is to improve the map, by (in this case) resolving notes. Being hasty to close notes for the sake of it, to achieve the illusion of a zero-count of outstanding issues, isn't constructive.

What's the harm of leaving a note open?

“I was local at that time and could not assign the note to anything for sure.”

You didn't specify this in your earlier comments.

Would you object to a second opinion?

When in doubt, map all the things.

“So, could you agree to close this again?”

To what end (before it's resolved)?