If you're using a mapped domain on your site, members resetting their passwords will see a security certificate warning (see this FAQ entry for more information). You can resolve this warning message by modifying your e-mail templates to direct members to your Squarespace URL to reset their password.
From [Website Management > Structure > Website Settings > Email], choose the Password Recovery e-mail template. Replace the existing password recovery variable:
by adding this new variable:
This will use your Squarespace URL instead, and will eliminate the security warning.
Note: Amending your e-mail templates is a feature available with the Unlimited package. Please exercise caution when making changes, as this can affect information added to your messages.