It depends what you mean by 'damaging'. Removing the signature would mean grinding off maybe 1mm of glass, which is not very much - but would leave a flat area. More important is the risk involved whenever you grind glass off a paperweight: there may be significant stress within the weight, which can then be revealed as a catastrophic - often terminal - crack during polishing. I have seen this several times with Ysart / Vasart weights ( I have two nice Paul Ysart 1930s flowers which looks great, unless you see them side on - then you see they are riddled with huge cracks, post polishing, and might fall apart at any minute.). I think it comes down to the glass they used and the poor, badly controlled annealing process. Antique lead glass weights are far more tolerant of polishing, as are modern paperweights - but the cracks run much deeper into modern glass.
(If anyone wants to be bored by the intricate physics of Hertzian ring cracks (which is what bruises are), just let me know. It was part of my post-doctorate work on diamonds, and I used to know too much about it.... Don't Google the phrase unless you feel strong (really, don't), but if you must dig deeper, check out this article Hertzian fracture
- it describes the theory of bruises in brittle materials like glass.