Bill
Shops are often reluctant to pay out for removal because they know they will come back again.
However, if you can suggest that once you have removed the gum they can buy a gum removal kit from you (Spiker, freezer and say Citrus gel) and then train them to remove the individual pieces of gum as they appear on a day by day basis then it no longer becomes a daunting and long-winded to job to remove them because it doesn't build up into a big job.
Then the next time the carpet is cleaned they'll ask for you because you've helped them keep the problem from recurring and secondly you won't have any gum to remove-just a carpet to clean.
This has sometimes worked for me. And sometimes they've just ignored the kit I've sold them and got me back to clean the carpet and remove the gum. :
