BuddyPress.org

Looking at the activity entry file that time stamp is part of the bp_activity_action() template tag, looking that up in core bp-activity-templatetags.php and it shows bp_activity_time_since applied to $content for that template tag.

A quick and possibly incorrect attempt to remove the time stamp:

function remove_activity_timestamp() {
$content = '';
}
add_filter('bp_activity_time_since', 'remove_activity_timestamp');

This works but I feel it isn’t really the best approach so would prefer one of the more experienced chaps to advise if a better or correct approach exits.