I think this one is going to have a messy answer. However, since you write that they have authorized you to use their logo (especially if they've already shipped/sold goods to you for resale), I'd argue that they have already used the mark in commerce in the U.S. (and have you already had some sales?). So, they probably have common-law trademark rights already (in the U.S., trademark rights flow from actual "use of the mark in commerce", not from registration). If you're the sole source, those rights may be limited to the area in which you have sold the goods; if you're doing internet sales, that might be national, but if you're running a mom-and-pop grocery store, it would probably be your immediate area (however far people travel to get groceries, plus a buffer zone for your "natural area of expansion").
I'd recommend that your supplier get the mark registered federally so that they don't run afoul of someone trying to hijack their mark. While they could still overcome that, it could get expensive for both sides.