Thats a Molex connector or knock-off.
The contacts are held in by little bits that spring out - if you just yank you'll ruin the contact, the housing or both.
The official tool is basically a semi-circular (or circular) bit of tubing, thin-wall, just bigger than the connector. But it can be released with any thin, stiff, strip of metal and some care.
I don't know that I've ever had the "proper tool" but I've certainly changed a few. If getting a proper tool you'll need to know the size of your contacts.
At that point you'll have a contact with wires crimped to it. You either crimp on a new contact (of the correct size and gender), or you splice your new wire to an old wire that's going away with the bad part, or you would be trying to loosen the crimp and reuse it, which may not be reliable. If you're going to end up splicing wires anyway, no need to actually remove the contact from the connector.