RESTful: almost correct usage of HTTP verbs to implement something that has nothing to do with REST. But it sure sounds nice.
I also hate this nitpicking, but it's clearly not going away so you're better off not inviting it by using the term incorrectly.
If I am 100% REST then I would say "I have a REST API". If, like most companies, I am not following all the REST conventions then I would say "RESTful" api.
The moaning about "RESTful has been hijacked by people who don't know REST" by the REST purists always struck me as strange when they could have made that simple distinction.
I borrowed RESTish from Dan Savage's concept of "monogamish", meaning a relationship that conforms generally but not rigidly and precisely to the norms of monogamy. As such, a RESTish API conforms generally but not rigidly and precisely to the norms of REST.
If you aren't following REST conventions, its probably better to say "HTTP API" and not make any claims at all related to REST (except, perhaps, negative ones like "non-REST".)