Grey 0.5 Weight Tools - Can't bank?

There are a number of tools in the crafting section of my inventory (from a Carpentry Hammer to a Tanning Knife) which have grey names. It appears I can't put them in the bank. I don't think they're rewards, since they are in my inventory not the bank (where the rest of my rewards went upon claiming).

Is the idea that we all always carry a reasonably complete crafting toolset? Are these special in any way?

 

You have to right click and Unequip first

 

Thanks, @Kevin2437!