1. Hide dynamicly the module "div" from screen by clicking X in the module corner (use jquery 1.8 as it is loaded by template). The X has been added in the file public_html/homepage/templates/yoo_subway/styles/homepage/layouts/[url removed, login to view] which is warp override file.
2. Update the string in table JOS_FUA_USERINDEX for the user logged in by using AJAX call in the background (this table controls the display of the modules by the front-user-access component). You maybe able to use SQL replace function for -- ,"XX" where XX is the module ID. Module ID will never be the first item in string.
3. Make sure the X in the module corner is only displayed in modules in the homepage (user is logged in and in the homepage)
4. Make sure user is only able to remove his own modules and not any other user (security !)