This style of pewter box is very controversial in the collecting world. It is felt by many collectors to be a means of shuttling leeches from the apothecary to the patient during house calls. A version is on display at the Wellcome museum that has the word "LEECHES" inscribed into the case. This piece didn't enter the collection until 1970. Many prominent dealers in the field of medical antiques believe the mark is a fake. The collector has to make this decision on their own knowing that no known ads have been identified for the item to be used as a leech carrier and that advertisements can be presented showing all sizes as brush cases. Be aware that many forms of fakes are based around this general design, some as utilitarian as butter dishes.
More traditional French style leech carrier. Note the holes in the lid designed to allow gas transfer. It is likely that the bottom of these carriers would be lined with moistened moss to allow the leeches to survive during transport.