BuddyPress.org

@nebuchadnezzar no need to modify anything inside BuddyPress core files, You have to modify template files inside your child theme.

Copy BuddyPress folder from your parent theme and paste them into the child theme and modify inside child theme at following path

buddypress/members/register.php or
buddypress/registration/register.php

You can check following for reference

Template Hierarchy