The first two are new to me, so thank you, I'll read up. The third succinctly explains a quirk I've never bothered to check the legitimacy of, so thank you again.
With your changes, that brings us way below the character limit, sitting at 208 characters with the <body> and <script> tags the challenge dictates.
I had to rejig things to use parent.append(child) as it doesn't return the element, but using the child.remove() method directly means there's no parameter and therefore one less character there, so it all balances out. I also had to rename the event variable as it caused a scoping conflict for the variable `a`.
With all that space left over you could certainly add in the clear all and strike-through behaviour properly. Maybe even some real state!
Updated fiddle: https://jsfiddle.net/2z0bus8d/1/