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There's a clip on the bottom of the connector that you need to push down as you're pulling it apart. In this picture the clip is on top so you can see it better but you just need to push that down as you're removing it.
No tools needed to release the coil connector.
Get a good look at one of the front ones to figure it out.
Push up the button on the bottom of the connector and as you are holding the button depressed, pull it away from the coil.