Claiming a trademark is distinct from registering a trademark. You can claim a trademark by just saying "this is our trademark." That will typically be done with the "TM" symbol. Registering a trademark means you applied with the USPTO to get a registered trademark, and it was granted.

You are correct in that they don't make an explicit claim, but I'm not sure if trademark law actually requires you to do that. It would certainly make everything less messy.

> I'm not sure if trademark law actually requires you to do that.

It definitely does not. It certainly could influence a court decision (there's always a degree of uncertainty with any court case), but you absolutely can defend a mark that you have not explicitly claimed or registered, as long as you can demonstrate sufficiently widespread prior use.

If you search the trademark database it looks like they only filed for an application 5 days ago.

I don't see this as getting any more interesting than Instagram ignoring this plea.

> I don't see a trademark claim for the name Bolt on their website.

This is a very common misconception. Trademarks do not need to be registered in order to be defended (and even registering a trademark does not mean you can defend it).

Registering a trademark might have prevented this situation, but only if the Instagram lawyers took the time to search the USPTO database for marks matching "Bolt" (but even then, it's not a guarantee since (A) the search interface is pretty bad, and (B) they may have decided to go ahead and use it anyway).