Pretty much as Simon said.
When giving the quote, quote for not removing the gum but make the point to the prospective client that you are "guessing" that the gum removal is perhaps one of the main reasons they want the carpet cleaning. As such make sure you know how much more you are going to charge. And don't forget a dirty carpet will often hide quite a lot of gum which will only become apparent as you clean the carpet.
Going forwards, after all, you want to get this as a repeat job, offer to train the cleaning staff on the best way to remove gum. Make the point to the owners that the owners will be paying the cleaners a fraction of your bill in cleaners wages to keep on top of it; the carpet will look nicer for longer; your job will be so much easier (and perhaps cheaper) when you come to clean it again. And without the gum the client's premises will look far more attractive and cared for as well.
In summary, you may have to remove it this time-but get paid handsomely for it, but if you work well with the client you won't have gum to remove in the future and will have a (far nicer) repeat job in the future.
Rog