you have a problem
acrylic is man made synthetic fiber it stretches in heat and moisture;
and you have wool which is animal fiber with lots of microscopic tiers; which gum will stick to;
so any dye on wool will be oil soluble; and water will shrink the wool;
and you said you try to get it out as much as you can; which means you used your fingers;
by using fingers against the gum; you pushed them toward the bottom of the clothes; rather than surface;
had you not touched it;
and you said; daughter; which means your jumper is not beige; which is natural color of wool; which would be better; under the circumstances;
which means your jumper has dye on it; since its christmas present;
thats the assessment;
freezing it wont do because? we know its not on the surface but dug in;
and usual hair spray; baby oil wd40 won't do because? your jumper has colors; it will bleed when it get on your jumper;
its acrylic; which means its dry cleaning; and its wool; so your dye will be soluble; either way;
problem is getting oil out;
getting the gum out is not the problem; gum comes off with oil easy as pie; walk in the park;
you need oil to get the gum off; but once it comes off with oil you need solution to get oil out;
so question is what kind of oil that be safe ;
so test it; get some of following oil; extra virgin olive oil; vegetable oil; corn oil; and test it on jumper;
check the pocket liner see if its same material; some are; some not; if it is; you can use pocket liner to test it;
if thats not available then look for hem; ; there should be extra material
since its jumpsuit there should be inside material at lapel;
so tested place where it can go bad and not show;
these oils will get the gum out; and dishwashing liquid will get the oil out;
so you need to dilute dishwashing liquid and test it too ; by putting towel under it drop few drops and see if it bleeds; unto towel;
just because it bleeds does not mean its a damage; excess comes off from all clothes; so don't worry if it bleeds
its a damage when area becomes lighter;
there are times when it will bleed and not get lighter; so its nothing to be concerned;
then dab it with terry cloth towel to dry;