I recently replaced my front door bell because it kept going off without being pushed.
When I removed the old one I noticed some type of diode or resistor thingy behind the button linking the two leads together. The new button did not come with this thingy. Now when I press the new button it starts to set off the chime but when I release the button the chime stops. Do I need the thingy on the back? And what is it exactly because I dropped the old one and can't find it now. Thank you.

Sounds like some sort of capacitor that the chime needs to continue chiming after the button has been released. Best I can offer is to find a button for that brand of chime. Is there a label inside the chime with the make and model number?