Jeff wrote;
mineral turps is a solvent for blutack - then you will need
something to
remove the smell of the turps

Turps or white spirit will remove blue tack or chewing gum, but you do
need to be careful about the backing material of the carpet. The
solvent may attack that, or the bonding agent.

Got an offcut to try it on?

If it seems OK after a few hours use it on the carpet, then dab with
tepid water & washing up liquid. Blot up water with kitchen roll.

Plan B. Ice in a plastic bag, get the blue tack really, really cold
and it should crumble in to powder with a little gentle scraping.

Dave