The formal name for IGMP join/leave is IGMP Membership Report. An upstream router that deals with IGMP on a multiaccess network is called Querier. It does indeed Query all hosts (224.0.0.1) periodically for their actual group membership status.
As multiaccess network could be quite large, this may trigger an influx of IGMP Membership Reports that may overwhelm the network or a Querier itself; given the nature of multicast it does not really matter how many hosts on a network listen to the particular group, just one would be sufficient to continue streaming this group on an interface.
For that matter upon receiving IGMP Query all hosts start a random timer and first one to expire sends its Membership Report to 224.0.0.1 for the Querier and others to hear. If host has heard that it's groups have been already reported, it cancels the timer. The architecture is built so that in most cases only a few hosts will actually respond to Query. The host that has reported a group during this process is called Last Reporter for this group.
As you can see the upstream router has no idea how many clients listen to a particular group. So when host sends Leave Report the router does not (and should not by design) immediately stop this multicast stream on an interface as there could be other clients listening to it. Instead it sends IGMP Specific Query to this particular group (i.e. 239.0.0.1) to trigger some other clients that listen to it to send back their Membership Report.
As all of this Query/Report stuff is sent asynchronously and unreliably over multicast there is a non-zero probability that this Specific Query might not get an immediate Report back due to packet loss or other issues, so the router by default tries to send it twice (over two Query Intervals) and only then the multicast group is pruned on an interface and traffic flow stops. The same applies if for a standard Membership Query (on 224.0.0.1) the particular group is not reported back twice, this might happen if a software or hardware malfunctions before being able to send a Leave Report for a group.
The Scope as such is a multicast address scope that roots back in the days of old and glorious Global Internet Multicast Routing Dream and specifies the area where this group should circulate, 0 means local network in IPv4.