I agree with "Auspicious" only so far as believing that adding a tip to the bill without advance notification on the menu is not acceptable (to me). However, I would simply take it off the bill, pay the remaining balance & leave a cash tip for the waitstaff. Let the management decide to come to me or not -- I don't need or want to talk to them about their business practices -- let them take me to court if they wish to defend their added tip.
In my opinion, an advertised "mandatory gratuity" in & of itself is not "bait and switch". It is, to me, much the same as a no tipping policy or a "service included" statement on the menu -- it just changes how the math is done. As long as I know in advance, I'm ok. Either way, I'll have to assume that the business takes care of its operation (including its employees). If anyone cares, I prefer to pay the bill & leave a tip of my choosing. For me, its a more direct way of knowing that the front of house staff is making a living. Of course, this is based on traditional practice in my home area and is full of holes if/when I think about it too much (i.e.; why don't I care that the back of house is being compensated fairly? why do I want to intervene in the business model at all?). At my age, I find it easier to just continue to do what I've always done, think about it as little as possible and take headache meds. when I don't follow my own advice and write posts about it.
By the way, the "no tipping pricing models as in most of Europe" no longer exists as a general guideline for non-locals & barely for locals in most places that I've visited. Although no one can agree on what's expected from American tourists anymore, I can say that I've watched lifelong residents of Florence, Rome, Paris, Lyon, & other places put down 5-10% (& even "round up" in places where "service included" was clearly written on the menu), while I've seen dirty looks given to other tourists who left under 10%. Things change.