What's this w-shaped ebony item from my grandma's violin case?
Possible it's not violin-related.
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It's a mute. It clips onto the bridge. Damps the sound.
This is the traditional type. There are others:
As others have said, it's a mute, designed to be clamped on the bridge with its fingers between the strings. I warn against extended use of it for practice reasons: the violin takes considerable time to recover from longer use and redevelop its full tone.
Also it changes the response of the strings to the bowing and makes tone and intonation problems harder to hear. So (sadly for neighbors and relatives) it is a particularly bad idea for beginners still working out their intonation and tone control.
This goes doubly for the much more thorough "tone wolf", basically a rubber(?)-filled metal barrel with similar clamp-on fingers which is only intended as practice mute.
The mute depicted here is a stronger variant of a mute you'd use in concert for "con sordino" passages. A mute that looks like a rubber disk and sits on the middle strings on the tailpiece side of the bridge when unused tends to be more practical in use (though not as strong in effect) and does not squeeze the bridge to the point where it takes significant time to recover. But since it changes sound more than volume, it just serves as a concert mute, not a practice mute. And when you change the sound of a violin (by adding mutes or using different strings), that does change the body's response as well, so even here you get bounceback effects when using the mute for prolonged times.
This is called a "mute". This can be put onto the bridge (the teeth go between the strings) to get a soft, dampened sound.