Looks like the brake shoe material delaminated and fell off.
This shouldn't affect getting the rotor back on: the inside 'drum' on the back of the rotor shouldn't catch on the parking brake shoes, and should seat on the hub. The caliper bracket shouldn't come into any contact with anything related to the parking brake.
Make sure the rotor in fully seated against the hub. Use your lug nuts to keep it in place temporarily.
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