Exercise calories

You won't get a single answer here on that!

If you are using the MFP method then yes you should eat something back otherwise you are increasing the overall calorie deficit and will lose weight faster than planned. That might mean insufficient nutrition and muscle loss which will not help your health or achieve your goals longer term.

How much seems a matter for constant debate. Problem is that the exercise calories may not be accurate for you. I measure most of mine on a heart rate monitor but get the odd one from the MFP database, always eat 100% back, and have consistently lost weight faster than MFP predicts for someone lightly active. My solution was to stick with that but manually increase the calorie goal MFP comes up with. But it's said the MFP database overestimates the burn for most people and therefore you shouldn't eat all those calories back, 50-75% is often quoted. That's probably true for others.

But the whole system is based on estimates whether it be what you burn, the amount of calories in the food you eat or the amount you actually absorb from that food! So best to test it out in reality I reckon. Keep yourself sensibly well nourished and do eat at least some of your exercise calories back. If you keep your approach consistent, you can see what actually happens over a few weeks to your weight. If you are losing weight too fast or too slow, either adjust your approach or change the calorie goal itself.

I don't eat mine back because that leaves me a margin of error in miscalculations from MFP's food database. Remember when you use MFP's exercise database, it usually estimates calories burned higher than they are, so I believe most people eat only half of them back.