Thanks!

No, the files don't have links to external Artwork, those links are within MediaMonkey. However there is no setting to not include Artwork when converting.

I'm not sure if we're talking about the same thing, so I wasn't clear.

The Rip process is copying the JPGs and PNGs from the source folder and copying them to the destination folder. I'd rather they didn't get copied.

If it's embedded in the FLAC then I can understand that the Rip process embeds them into the MP3. No problem there.

Your use of the word "associated" makes me think that the FLACs have a pointer to a separate JPG or PNG file. Is this correct? If so, then my dilemma is understandable, and I learned something new.

No, if Artwork is associated with the FLAC it will be with the MP3 files. However you can remove the Artwork from the Properties > Artwork tab from the MP3 file properties after the conversion.

Is there a way that I can RIP a set of FLACs to MP3 and not have any album art copied?

I right-click on a Playlist... Send To... Rip/Convert... Destination Directory
I found nothing in Configure or Settings, and nothing obvious popped up under Tools... Options