Hextech Craffting Reroll tells you that you can reroll permanents, but there is no option for that.
Final Edit: I got confused because shard upgrading creates a skin permanent that is automatically added to your inventory, So I initially thought permanents refers to all the skins and champs you have unlocked.
But there actually are other methods to get skin permanents that remain withing hextech crafting and those can be used to reroll.
OP: Check out the reroll option, it says you need three shards or permanents to reroll.
This clearly says that you should be able to use your unwanted permanents to reroll into something else.
But since you have no access to your permanents from the Hexteh Crafting Screen, it's not possible to actually add them there.
So did someone just place the wrong tooltip there, or is that actually intended?
Edit: Ok since the first three responses seem to talk about shards by calling them permanent, let me clarifiy: That's not what I mean.
When you open the Box you get a "shard". The "permanent" you get by upgrading a shard with some essence.
However this "permanent" doesn't seem to be anything that's special to Hextech crafting as it goes directly to your "permanent inventory" with all your other skins.
Now the reroll page tells you to use shards or those perments, but there is no option to get the permanents back into the Hextech Crafting.
Now of course it would be dump to first upgrade a shard into permanent and then reroll it, but accidents happen and there are also unwanted permanents you got from Mystery Boxes.