Plumbing – What do I need to remove and replace this recessed faucet aerator

I've got a bathroom sink faucet with a recessed (cache) aerator that needs to be cleaned or replaced, but seems to require a special tool to remove it. There is no obvious branding on the faucet, so I don't know what removal tool to ask or look for.

I've tried some of the "standard" removal keys they sell at the big box stores, but they don't fit. Those keys seem to be a little too big and you can tell that the tooth pattern is not quite right.

I've included pictures of the faucet, the aerator, and a key that does not fit.

Wondering if anyone knows what kit or tool I need to remove and replace this aerator?

Image of faucet here:

Close-up of aerator:

Example of key that did not work:

+++ Update +++

Thanks to @Alaska-man, it turns out the tip of the faucet itself was threaded and, once removed, gave me direct access to the aerator (which is not itself threaded).
Don't know why I didn't think to to try this. Perhaps because the visible part of the aerator had grooves that convinced me that it was itself threaded.

Images of tip and aerator removed. Also, it's apparently a Delta faucet (discovered after removing tip and observing lettering on underside).