What is ‘for-picking-up hand’ 提手旁 in the end?
We write 手 for ‘hand’. Why? Does it shape like the last part of your arm? You may first draw the top stroke as the middle finger and use the vertical line as the main back-bone of the hand（or arm?）, then add the bottom two horizon lines to symbol the remaining four fingers. It is fun if you gesture out the shape of 手 with your own hand by yourself! Here I can sense that the ‘hook’ of 手 showing off too much strength when you try to pick up some heavy object from the ground. In other words, one of the functions for the hand is to carry things with strength like a hook.
Furthermore, many Chinese characters include one hand. Such as：提（pull up）, 打（hit or beat）, 扫（sweep）， 挑（choose）, 抱（to arm）, 找（look for），投（throw）....
These words have the same component called ‘for-picking-up hand’ since you can not finish those actions if without hand! You may take it as a changed form of 手 which has ‘lost’ the top finger; Or let's think it in this way: It is a version of the up-down-side of 手with the hook as the middle finger and the remaining strokes as other fingers for picking-up.