I’ve always used another piece of blu-tac. Hold the second blob and dab it against the first to help lift it. This takes a bit of time.

Carpet stain remover? Or if it’s only a little bit maybe cut it out?

Rub with an ice cube so it hardens. Should be able to pick it once cold.
Have used this method with slime.

Do NOT use nail varnish remover!!! You risk melting /destroying your carpet as true nail varnish remover has acetone in, a solvent which will part melt carpet.
Tiny tests in a discreet hidden section recommended, but essentially you have 2 issues to tackle with blu tack, firstly the sticky blobs, but also the oil in it which if left will stain. (think of the posters you put up with blu tack that were there for long periods – that greasy mark it left?
Your best bet is to freeze it with ice cube or similar, and then when dry, dry pick out or scrape off what you can. (scalpel or craft knife blade from art shop.) Try to remove the bulk of it at this stage.Then, and only then , can you try to tackle what’s left with a solvent/de grease stain spot solution, but be very careful . Depending on pile length, you may have to trim out any very bad bits, but hopefully not.
Oh, and I stress the avoid nail varnish warning as I work with acetone and stained/soiled things for my job – objects conservator and restorer!

Freezing works on most fabrics – since you obvs can’t stuff it in the freezer, maybe try using an ice cube to harden the blu tac so you can get it out.

The orange brand make a spray on carpet stain remover that might be worth a try, I’ve found it very good on other stains. I’d try nail polish remover (check in a corner first that it doesn’t discolour).
I’d stay away from any oils on carpet.

Excellent answer from Ellen; quite comprehensive.

Blu Tack can be removed from a carpet with white vinegar. Apply the warm vinegar to the stain with a clean, white cloth after warming it on medium heat. If you give this 15 to 30 minutes, the stain should weaken and become soft enough to pull out.
Other options are
Citrus cleaner.
Acetone.
Laundry detergent.
Olive, vegetable or eucalyptus oil.

No tips; removed all carpet and went with an alternative that can be easily cleaned.

Try to lift as much as you can, even with tweezers if needed. Possibly isopropyl alcohol will help lift the rest. It was able to remove sticky residue I had on furniture. As someone else mentioned, test it first incase it stains.

Try a good sticky tape over the area and see if that helps pull any of it up

Gently scrape the blue tac with a blunt knife or credit card. If any residue remains, a small amount of rubbing alcohol on a cloth can help remove it. Test the alcohol in an inconspicuous area first to ensure it doesn’t discolour the carpet.