I want to know if there is way to check if the integration was removed from board integrations or not using API.
Welcome to the community. If you are developing your own integrations you can use a custom trigger that has subscribe and unsubscribe events. The unsubscribe endpoint will be triggered when the integration is removed from the board.
Can I listen on unsubscribe event when while i’m using the predefined triggers ?
No, unfortunately the predefined triggers are not configurable with an endpoint that listens to (un)subscribe events.