Need advice on flooring

[Pute]

We own a converted ground floor flat. The couple who own the upper floors of the conversion are selling and all was going well. The buyer found the clause in the lease that the level above ours must be carpeted. They are now asking for a letter of consent to lay wooden flooring with special sound proofing as the buyer has medical issue.
Questions:

1. Innumerable posts keep saying that it's not recommended to allow removal of carpet but any of you experienced anything similar?
2. We don't want to be the reason for the fallout as we have been good neighbours to each other.Any idea if there is any better way to deal with such a situation?
3. In general, should we sign such a letter of consent and then what happens to the conditions on the lease?

Any suggestions are highly welcome!

In our last Victorian conversion property, our upstairs neighbour changed the carpets to engineered wood without our consent. We didn't say anything at the time as he was lovely and we had a great relationship. It didn't bother us, as our flat was a ground floor/ semi- basement maisonette, with bedrooms downstairs (basement) and living areas on the ground floor. When we were in the living- room we could hear everything. Luckily they were usually quiet and not having parties. I wouldn't give my consent to this, as you don't know how noisy they will be. Especially if they are right above your bedroom.

Ask for information as to the nature of the "special soundproofing " - it's not impossible that it would be just as good or better than carpet