How to remove blu-tack stains off the wall?

If the stains are in the wallboard reprime it and paint over the primer.

From the makers of Blu-Tack:

Citrus based stain remover is the best. If the walls have been painted sometime ago, they can become porous which will suck the oil out of Blu Tack. In this instance, you will need to clean with Sugar Soap and generally repaint the surface. Source

^^^ “Sugar soap” = TSP (tri-sodium phosphate), available at hardware stores.

This isn’t entirely on topic in the form of providing a solution to the question at hand, but should help in the form of a preventative measure for future reference. If you take a bit of blu-tac and warm it up in the palms of your hands, then, using controlled, small circular ‘dabs’ that are firm but not hard on the blu-tac already stuck to the wall with the warmed up blu-tac between finger and thumb, you should be able to remove the blu-tac without leaving a stain – or ripping off shreds of wallpaper. I’ve done it and it works for me, but it may not work for others – so don’t take it as gospel.

This may sound strange but lysol spray on walls gets rid of lots of different stains. Only be careful, it can also remove paint if it is water based.

Salt and water! These worked great for me.