User concerns over twitter OAuth. Ideas anyone?

So our newly launched app (demandspot.com) lets users sign-in using twitter OAuth (sign-in with twitter button prominently displayed). However, this isn't well understood and it seems like people are concerned of "giving us their twitter password". Does anyone have experience with this issue, or ideas on how we should explain the process and try and alleviate user concerns? Our target audience is twitter-using real estate agents, so keep in mind that this isn't the most tech-savvy population.