Nadsab
the lines I assume you are trying to delete are the diagonal ones, however these are part of the objects make-up and occur sometimes when something is created in another program / format and opened in TC, such as 3DS files, normally they can't be simply deleted whether you explode the group or not, yes they can be deleted once exploded down to a poyline but thats no good if you want hidden line or other renders.
If they are an annoyance, then the best way I know is to use the original object as a template and re-create the part in TC's own format, this is the same in the pro version of TC, indeed changin your object into a pro ACIS solid actually makes it worse. occasionally re-saving in another format then opening that can help, but its trial and error.
Andy