Looks like a type of "Stinkhorn" to me. If it's like mine, they stink really bad... such that you can smell them 20 feet away. I'd say "Kill it ASAP", but from what I understand it's just a manifestation of the fungi that are already in the soil. But, at least removing it would prevent the flies from pollinating it and hopefully slow their spread.
-Glenn

Glenn is exactly right. I get them in fall, not spring. Just get rid of the stinkhorn, after you stop giggling at its name! Mrs. G

The Latin name of the common stinkhorn is even more comedic, "Phallus impudicus". Yours may be a related species, but the appearance and later smell are the only good reasons to get rid of the fruiting body of something that decomposes old wood and forms beneficial mycorrhizal relationships with plants.