I did a brief Google search. If I am not mistaken, that connector is a Metri-Pack 150 pull-to-seat. You're not going to be able to remove the terminals. It's not the more common Metri-Pack 150, which is push-to-seat.
Push-to-Seat
With the more common push-to-seat terminal, the terminal is installed through the back of the connector. To remove the terminal, you insert the terminal release tool in through the front of the connector, release the tang, and then you remove the terminal out the back of the connector.
Pull-to-Seat
With the less common pull-to-seat terminal (also known as Metri-Pack 150.2), the terminal is installed through the front of the connector by pulling the wire/terminal through the front of the connector until it locks into the connector cavity. Unfortunately, you cannot remove the terminal once seated. The easiest way to repair the circuit would be to cut off the old pigtail and splice in a new pigtail. You must remember though, you have to install the wire and terminal through the front of the connector. This is important if you are doing the terminal crimping yourself. However, if you buy a pre-made pigtail, then you will only need to worry about the splicing.
Watch this video, and at the 5:14 mark, he reiterates what I stated about not being able to release the terminals.
Think about it this way. If the terminal is installed through the front, then even if you happen to release the terminal and remove the terminal through the front, you still have the connector housing sitting on the wire. You can't remove the connector housing unless you cut the wire somewhere. That's all that it comes down to.
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I re-made my entire ground circuit for my AC compressor in my engine bay as the previous owner had spliced into it, and I wanted to restore it to factory condition. It was a relatively complex circuit, with several branches. I did all the wiring, splicing, and terminal crimping myself back to factory condition.
It included a couple pull-to-seat connectors, including one at the ABS module and another around the AC compressor. I have hands-on experience with these pull-to-seat connectors.
