How is the business appearing in the results right now?
Are the two dupes both showing up as unclaimed listings? Are there other dupes that should be dealt with as well?
Depending on what's currently showing up, a flat-out "remove from Google maps" probably isn't your best solution. If there's conflicting data that Google is pulling from, at best it's going to be a temporary solution that will pop up the instant you tell your client "all fixed". At worst, it might suppress too many things, or suppress the wrong data.
I'd track down all the dupes that exist, AND where the upstream data that's causing them is coming from first. Then figure out whether there's any relationship between the pending listings and what's showing up (i.e. did someone attempt to claim already existing duplicate listings, or did they create them manually?). Once you've done that you should have a pretty good idea of what is what.
Unless you can get a miraculous intervention from Google Places help, removing them from your account and claiming already existing listings is probably what you'll end up doing. After you've cleaned up the upstream issues that messy data is causing.
Edits by users could be used to make sure the information on duplicate listings is completely identical. That's the one way I've managed to get Google to review duplicate listings and merge them via the "report a problem" link.