BuddyPress.org

Since it’s theme specific, your best choice is to create a child theme and override that template part when you don’t want to see the image. (There are lots of conditional you can use, like is_buddypress() which returns true on a BP page.)

It’s extremely unlikely that there will be a plugin that changes one aspect of a specific theme.

Child themes: https://codex.wordpress.org/Child_Themes