I agreed on Rentokill, as no point you doing now which only concentrate on one area which you will remove and replaced with Concrete, and will move to other place when reno start.
What you could do now is go hardware shop and buy the termite killer which cost RM80 and spray around your staircase and area around, or could spray the whole house if not one around. This will kill those termite if they can out. You also should inform your contractor to spray those wood when they start doing reno on your staircase so that they can’t ran anyway.
During the reno, you could ask them to spray around the house / roof area to prevent termite coming, or get the termite system in place.

Agreed....that the reason I put "could spray the whole house if not one around". you will run out from the house.

Just ignore your neighbour, and do what you need to do.
your role is inform them your house got termite, caustion step shall then taken from them, because is not somehting your could do.