The filter oil would not harm your motor. But too much oil on the filter will cause your bike to run very rich, so you may foul a spark plug. Basically, it has to suck harder to get the air it needs. When it sucks harder, it pulls more fuel in from the float bowl.
Wring it out (gently) and wrapped with paper towels or even newspapers until you get the excess oil off and you will probably be good to go. It is still over oiled, clean it like you do when it's dirty and re-oil.
FWIW, the No-Toil system with a special oil that gets cleaned with a powder dissolved in water is great! In the old days, we used gasoline to remove the filter oil, but the No Toil system is waaaay better.