If you’re using Timewarp in the FCurves window you must select all the objects and all the Transformation channels on those objects you want to apply the Timewarp to.
So in your case:
Left-Click in an empty area of the Character Controls window to select all the FK and IK controls
Left-Click Select the Translation and Rotation channels in the FCurves window
Enable Timewarp Display
Create a Timewarp
Apply the Timewarp to the selected channels
Edit as you have been doing
As other have suggested, you can also use the Story tool to reverse the animation:
Turn on Story: Turn on Story mode in either the Transport Controls or the Story Window.
Create a Character Animation Track: In the Story window Right-Click in the Action Timeline and select Insert>Character Animation Track from the pop-up menu.
Assign the Character to the Story Track In the Character Animation Track, select the characters name from the
Character drop-down menu.
Insert Current Take: In the Action Timeline of the Character Track, Right-Click and select Insert Current Take from the pop-up menu. This adds the animation in the current take to the Story tool.
Frame Clip: Select the clip and press f to frame it in the Action Timeline.
Reverse: Select the clip containing the animation you want to reverse. In Properties>Timewarp make sure Enable Timewarp is active and click Reverse.
I also have a tutorial explaining more about the Story Tool here: