Within the "Options" section of group-creation or group-editing window set membership to "Invite Only".
By default the system provides you with a "Generic Group Sign Up" form which people can access when signing up for a group (this form can be changed).
Approving or declining registrants who complete the registration form.
When someone completes this registration form the Group Leader will be notified via email and within the dashboard view of their One Church Software account.
Both of these notifications link you to the registrant and then provides an option to approve or deny acceptance to the group. If "denied" you have the option to email the reason(s) why.
If you choose "Denied" you have the option to send an email explaining why (see below).
You can fully customize that email including the subject and content.
It supports HTML so you can include links, images, emojis, anything you'd like. This will help you provide alternative options for the person to find their fit in another group.