Here's what Trulia Help says. Good luck. The first step failed for me because I could not find the "My Listings" icon. If you do, please share. Difficult website.
"If you have manually submitted your listings to Trulia you may delete them by logging into your account and selecting the My Listings icon from the top right hand corner. Click on the For Rent tab. Hover over the Edit Listing tab and click Delete. Confirm your selection."... more