The principle of opening up and polishing inlet manifolds is well known and proven.
I was doing just this sort of tuning to MGBs in 1966. The idea is to increase the smooth flow of the mixture by reducing the resistance caused by the cast surface on the inside of the manifold.
Having said that, two things would concern me about the offered item.
We used to match the head/gasket/manifold/carburettors at all the joints so there was a smooth and consistent size through the inlet tract, followed by gas flow checks.
You can not, in my opinion, buy parts to match the bits on your car precisely thus the benefits may not be achieved, you could in fact make things worse.
I would therefore be suspicious of the gain in performance they claim by just adding the part and I am not sure how "reflashing the ECU" will help.
I agree it’s a starting point in tuning but it’s certainly not a quick way to increase performance unless you machine all the adjacent parts to match, accurately.
If I were you, I would buy your Mum a nice present for Christmas and run the car on premium fuel, cost you a lot less than £250