That is a capacitor, a disc capacitor, to be more exact. I looked it up and found that it is used as a spark suppressor, presumably to lengthen the life of the EOS contacts.

I now enter, with trepidation, the realm of limited knowledge. What the hee haw, someone will correct me if I get it wrong!

There should be no effect or negligible effect on how ‘powerful’ the flippers are. I would reconnect the capacitor, but first I would test it with a DMM to make sure that it is still good. Not all DMMs can test capacitors, so your DMM, if you own one, may not have this function. Or you could just install a new disc capacitor across the EOS switch - they are cheap. I keep some disc capacitors on hand and are handy when I need one for a switch. You will need to to read the printing on the cap and learn what it means for the right replacement.

103 should mean 10 x 1,000 picofarads or 10,000 picofarads.

https://www.petervis.com/electronics/Ceramic_Disc_Capacitor_Values/Ceramic_Disc_Capacitor_Values.html

Disc capacitors may also be sold in microfarads. Don’t confuse the two. Converting 10,000 picofarads to microfarads yields .01 microfarads.

Don’t use commas. It seems to cornfuse the calculator.

http://www.unit-conversion.info/capacitance.html

There is usually a letter after the number signifying the tolerance. Do you see one on that cap or the cap on the other flipper?

@shapeshifter, that cap may not be original. I don’t see it on the flipper wiring diagram, page 22 of the manual. You might want to ask over at the Catacomb Club. Oh, I see that you already have. Never mind.