Android (e.g. Samsung, HTC, Sony): To delete an entire location history, open a group member's profile and long tap on one event to mark it, then click on the symbol next to the trash can in the top right hand-corner to mark all locations. You can then delete the entire history by tapping the trash can. If you only want to delete one message, simply mark it then tap the trash can symbol.

iOS (iPhone): To delete an entire location history, open a group member's profile and long tap on one event. An orange circle with a tick will appear next to each location. Tap the trash can symbol in the top right hand corner to delete the entire history. To keep some entries, deselect them before tapping the trash can symbol.