Hi,
Firstly, if these drums are new I would be thinking about contacting the supplier/manufacturer and asking for replacements. If you feel that the damamge has been caused since purchase then I think it depends on the severity of the damage.
This part of the drum is called the 'bearing edge' and drummers talk for hours about bearing edge design and shape because it is important for the sound of the drum. You are right to think that the skins could be damaged if the edge is substantially damaged. I could make some suggestions but without seeing the extent of damage it is difficult to know. You may get a better answer at this site: http://www.mikedolbear.co.uk/forum/default.asp?CAT_ID=1
but you will first have to register.
Julie Holding
May 2008