Ask Mr. Smarty Plants

The funny thing about Hibiscus coccineus (scarlet rosemallow), also called "Texas Star Hibiscus" is that, while it is native to the Southeastern United States from Florida to Mississippi, it is not native to Texas. At some point, someone in the nursery trade decided it would sell well with the name "Texas Star" and it has done so. That has nothing to do with your question, we just think it's amusing. Anyway, yes, go ahead and remove those stubs. We're a little surprised they have persisted. We always cut ours back in the fall, leaving the stub to identify where the plant is, but it usually just sort of disappeared after the new plant came up. Our suggestion is to start by giving the stub a gentle tug, rather than digging it out. Hopefully, it will break off, or just come up with vestiges of its old roots clinging to it. Digging out the stub could damage the developing roots of the new season's plant that is beginning to emerge. If you really want to clean up the area and make a new start, this plant can be propagated by root division. Since it is a late starter and does its blooming in the late summer, now would probably be a good time to do that. In doing so, you would be able to easily separate out the dead stems and roots, clean up any litter around the planting area, and perhaps throw in a little fertilizer (not high nitrogen lawn fertilizer, as that inhibits blooms), maybe some compost and you will likely have a whole bunch of vigorous new plants. 

Hibiscus coccineus

Hibiscus coccineus

Hibiscus coccineus

Hibiscus coccineus