When I uncheck the "Remember Password" box, Outlook gives me an error when synchronizing, instead of asking me for my Gmail password. It works fine when I tell it to remember the password, though...
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The dialog box pictured in the question has the title 'Test Account Settings.' In the 'Change Account' window, uncheck 'Test Account Settings' before clicking the Next Button. This will cause your client to wait until the next email sync to prompt you for your password.
Be aware!! Gmail IMAP has known issues with clients requesting to authenticate "too often." Among other things, this may flag your account to require passing a CAPTCHA to continue syncing. Visit https://www.google.com/accounts/DisplayUnlockCaptcha to attempt the unlock and then try your sync again. On this page Google specifically recommends configuring your client to remember the password.