Floral carpet roses typically grow no more than 21/2 feet tall. Depending on which cultivar you have, yours could be even shorter. Chances are those tall shoots have only leaves, or at least are very slow to develop flower buds at the tip. It's possible the rose is grafted, and the shoots you see are developing directly from roots below the graft.
Prune those errant shoots down to the ground (or to the canes from which they arise) as soon as you notice they're different from normal stems. If you allow them to grow, you'll no longer have a low-growing shrub. And if you cut them back partially, there's no guarantee that the canes will ever produce flowers. The only time you shouldn't prune them is in late summer or autumn, when pruning might interfere with the plant hardening off for winter.
Deb Brown is professor emeritus at the University of Minnesota Department of Horticultural Science.