Respite (formerly known as "mercy") is a flat spot or a jump added into your goal, depending on the goal type, which gives you a bit of a break after you've been charged. You can set how much respite you get in the "Commitment" tab under your graph, on a per-goal basis (you don't have to have the same settings for different goals).
Because whether you need respite or not is highly variable depending on your goal and your aims, it's totally configurable: if you need to get back on the horse right away, simply set your respite to 0, and your goal will be due again right away.
If you'd prefer to have a week of breathing space after you've been charged, then you can set the respite to 7. Even if you have the respite set to 7, you can always ratchet the respite away after a derailment if you want the goal to be due again sooner, so you might prefer to be generous with your respite and then tweak it according to your circumstances.
If you contact support to let them know a derailment was non-legit, they will typically remove the respite from your graph, putting you back on track. If you can't do your goal for a couple of days for some reason like sickness, let them know in the email when you're calling not legit!
Keywords: formerly "no-mercy recommits"