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So, this is designed around a one shot story, so the HP and Grit you have is all you have. In between stories, if using the same characters, I would just have them heal up completely. There isn’t a healing system set up. If you wanted to add some one use mechanical items, like a medical kit or similar, that could heal someone in a limited scope, I would say go for if it fits your game. 

I actually like the idea of there being no during-session healing - it sounds like that would add a certain amount of tension to the game. And for a multi-session game, campaign or otherwise, a downtime-refresh sounds appropriate, too (like a week or two of rest).