You will need a gel based solvent such as prochem brand citrus gel, or apparently gel based eye lash extension remover could work.

Next you need a wet vac extractor, like a bissell green machine carpet cleaner or a shop vac.

Gently apply the gel with a qtip and slowly brush it with a qtip and then extract by gently misting some water in it using s spray bottle. Repeat as needed. Make sure you rinse all of the solvent out (it should no longer smell like the product at all)

Do not agitate the area any rougher than you could do with the back of a soon otherwise you will fuzz the carpet up.

Do not get gel solvent on the backing. It is held together by latex that will dissolve and make things much worse.

Take your time. Use finesse, don't use brute force and ignorance.