Those are just new dogwood stems - no parasite or latent monster out to get anything.
It is quite common for trees (including dogwoods) to throw a sprout like this from dormant buds. It is a defense/survival mechanism against animal foraging/browsing, fire damage, and other unpleasantries that beset woody plants as they try to grow.
You should clip or break these off while they are little and tender, so the plant doesn't waste energy/resources on those stems.
