I've found that you need much more hand penetration to get the pump out of the clip than to get the connector off the top and more still to get the pump clipped back in place properly.
I'd leave the pump alone and just tug on the connector.
Maybe you could get further in with a bit of Vaseline?
Or if your hands are really too big you could wait outside the school gates with a pot of Vaseline and be ready with the line "Do you fancy earning a fiver sonny?"
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