MemberMouse does have a captcha validation option through Google ReCaptcha if you have not activated that on your forms yet. This can act both as a time deterrent, and block signups if these are submitted by bots. Our Configuring Captcha article can walk you through the process.
Otherwise, the best way to handle these type of signups would be to try one of the SPAM Registration plugins from the WordPress Plugin Directory. Some of them have different filter methods to refuse signups with certain characteristics, they may be helpful to you. When MemberMouse creates a member, it also creates a WordPress User, so those types of plugins will often work well to interrupt the signup process when something hits their filter.
We have an in-depth discussion about preventing bot signups directly through MemberMouse functionality on our blog How do I stop bot signups? . Take a look for some tips (in addition to Configuring Captcha)!