When a private member's bill goes to committee, the committee has 60 sitting days to study it. The committee is allowed to make a one-time request of 30 additional days to study the bill further. If the House grants the extension request, the 30 days are added to the initial 60. In order to obtain those 30 extra days, the committee must make the request to the House, which makes the decision to grant them or not.
In this case, the 60 days end on June 21. So if the House breaks for the summer before June 21, any days remaining from that 60-day period will be postponed to the fall. If the committee has not requested an extension by June 21, the bill will be deemed referred as it currently stands, meaning in its original form, since no amendments have yet been made.