Can I edit a walk cycle in Unity?

I have a character model with a walking animation but it walks forward instead of walking in place. I just want to remove or neutralize the z position so he stays still. Is this possible in Unity or do I need to do this externally?

It is possible. Duplicate the animation clip. The duplicated clip is now editable, next put your character with the duplicated animation on it into the scene. Open the animation window (Window/Animation). You can now edit/delete the z value on your characters root transform.

The only downside is that you will have to start this procedure all over again when reimporting your animation since it is only a copy.

Yes, if you duplicate the FBX and make it writeable, you should be able to access the curves of any animation clip from the animation window. That said there are no animation tools specific to walk cycles, except editing individual keyfames, trimming and looping clips and designing a state machine to combine and transition animations, so it might be easier in your source animation package to edit walk cycles.