Use a sewing pin or something similar to puss on the metal tab where the arrow points. Be gentle. You’re trying to nudge it, not kill it.
Press at the side of the tab closest to the plastic that’s holding it back. Once you’ve pressed it in past the plastic, the pin should hopefully slide downward (in the photo’s orientation). If not, you may need a second pin to push the connector’s pin down while keeping the tab down.
Note: if you push the tab too far, it won’t spring back to latch again when you re-attach the wire. The wire will just randomly fall out, connector pin and all. Also, if you press too hard, the pin may snap off. They’re not designed to be flexed too often.
Once the connector pin is out, I’d suggest soldering the wire to it. In fact, you may have to since the metal part of the wire was probably crimped to the connector and is probably still in there.