It can jolly be a strong growth of the rosebush. If so, the sterm should be a lot thicker than the rest and in deep blood colour.
However, it can also be a growth from the graft. The best way to identify this is to scratch to see if the sterm is above the grafted or below. You surely want to keep those above the graft and not below. Before you cut off the below graft growth, you can double check by comparing the mature leaf of the new growth sterm and the rest of other sterms. If they are the same, I suggest that you take a risk to keep it. If not, cut it straight away to avoid the stock drain off all the goodies in the soil.