Usually we worry more about them falling out then how to get them out..
It's not spot-welded, pinned or lock-set screwed is it b/c it should just pull/twist right out..
I used an open end wrench to carefully tap my new one into my new pump. Put the wrench's open end around the "collar" on the pick-up and hold the pump part "protected" in a vice and tap on the flat of the wrench carefully until the pick-up seats!! You will probably have to WORK at this b/c I sure did!!!
Then I put the pump back together, installed it in my motor that was up side down. Then set a 3/8" hex nut on the pick-up's high side making sure that it was above the level of my pan when it was installed. And then very carefully dropped my pan in place and screwed the four corner bolts tight. This caused the pan to push the pick-up into the proper "about 3/8" off the bottom position!!!
I then removed the pan and took the nut out and safety wired it so it couldn't fall out b/c I don't have a welder.
Just remember to remove the relief valve's spring in the housing if you weld it in place so you don't take it's temper out and ruin it.
Hope all this helps??