The latch is from the battery, yes? If so,this looks like a bit more than. Just the latch popped out sort of damage. For point of reference this is what the connector is supposed to look like. It seems like some of the outer bits have broken off. Which isikely why the latch won't set back in place.
Taping it from the outside is t really an option. It will need to be seated in the connector to make proper contact. You can probably tape it into place once it's in the connector, but it would be much better for the connector to be intact. Tape won't hold it as steadily.
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