That washer is called the hour wheel friction spring and it is supposed to be there. Every 4130 I've taken apart has had one. It keeps the hour wheel from dislodging and lifting upward if the movement is turned upside down (with a dial in place). A watch may function without one, especially if it isn't turned upside down often.
BTW as
@Digital. has documented the 4130 keyless might be easily reset without removing the dial. First check to see if the yoke for sliding pinion has lifted out of its sliding pinion detent and try to push it back with a small screwdriver.
If the setting lever is in the time setting position you can proceed as follows:
Bend a paperclip with a little hook on the end as shown. I sanded the hook end flat to keep from scratching up the parts, but the opening next to the crown is large enough to fit an unsanded paperclip, even a large one. If you hold the movement at eye level with good light you can see what you are doing.
You just need to put the hook behind the post on the setting lever and then pop the post to the other side of the setting lever jumper. This puts the keyless in the winding position and the stem will go right back in. Note the disappearance of the fat knurl on the stem in the final pic.