Rose Bushes - problems with the graft?

I have a rose bush - which is grafted to a wild rose - because of where we live. The part with the graft is living and I am getting lots of blooms. However, the wild part of the rose has started coming up - is there anything that I can do? I have been cutting down the wild part, but not sure if there is a better... show more I have a rose bush - which is grafted to a wild rose - because of where we live. The part with the graft is living and I am getting lots of blooms. However, the wild part of the rose has started coming up - is there anything that I can do? I have been cutting down the wild part, but not sure if there is a better answer. That wild graft is what allows the rose to grow in Colorado. Thanks
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