The growth coming up is suckering from the rootstock, so what you will have is rootstock.
What it is depends upon what rootstock your roses were budded on, but Dr. Huey is the most commonly-used choice.

It will make a vigorous once-blooming climber bearing many dark red blooms for a spring bloom.
I am told it blackspots badly where that is a problem.
It is, in most cases, virused.

Me, I'd shovel-prune it, but YMMV.

Jeri