First, you could try forcing the new options markup – which is easier to style, and is more accessible for assistive technologies – as follows (probably in your theme’s functions.php):
add_filter( 'bpges_use_new_options_panel', '__return_true' );
This may require additional CSS, since you appear to be using a custom theme.
If that doesn’t work, you can probably fix the messiness by applying some CSS that will cause the link in question to render inline rather than as a block element. BPGES has a pretty specific style targeting this element: #buddypress ul.item-list li div.action div a.group-subscription-options-link { display: inline; }
You must have something even more specific overriding it in your theme. Figure out what it is, and override *it* with inline styling.
As removing the text completely: The ‘change’ text is the only way to change the setting. If you remove it, there are no other buttons that will let users change their setting for the group. It’s not currently easy to modify this markup (especially the legacy markup) but if you really need to, you could unhook the function that BPGES uses, then copy it and modify it as you see fit. Something like:
// Remove BPGES buttons.
remove_action( 'bp_group_header_meta', 'ass_group_subscribe_button' );
remove_action( 'bp_directory_groups_actions', 'ass_group_subscribe_button' );
// Add custom buttons.
add_action( 'bp_group_header_meta', 'carlos4140_ass_group_subscribe_button' );
add_action( 'bp_directory_groups_actions', 'carlos4140_ass_group_subscribe_button' );
function carlos4140_ass_group_subscribe_button() {
// your modified version of ass_group_subscribe_button()
}