exercise calories

I personally do eat back my exercise calories but i often reduce the estimated calorie burn from exercise by as much as 50 to 75% to be safe.

If your activity level is consistent consider not recording calories burnt during exercise and just assume a larger daily calorie intake.

You do need to fuel your body, if your activity increases you will need to eat more. Fitness pal already gives you the calorie number you need to meet in order to lose weight, there's no reason to push it further and create a larger deficit.

Some more advice OP,

Exercise and eat according to your goals. I exercise 3 days a week with heavy weights and I don't burn all that many calories while doing it. That's ok though, I'm not lifting to burn calories, I'm lifting to preserve muscle while eating at a calorie deficit, my goal is to lose weight. Right now I'm doing cardio once a week and I use a heart rate monitor just to make sure I'm exercising at my target heart rate / appropriate intensity level for me.

You lose weight in the kitchen alone, make your gym time work for you and your goals.

IN THEORY - if everything on MFP was perfect, if you could perfectly measure calories/calorie burns, etc...

Then yes, you are supposed to eat your exercise calories back, in addition to your daily goal that MFP calculates.

The reason for all the 50%/75%/etc suggestions is that it's quite difficult to accurately measure actual calorie burns from exercise, so people eat back enough calories to fuel the workout, but not the full amount to try to incorporate the margin for error in calculations.

Yes I always eat them back, both when losing weight and also when maintaining.
Otherwise I would waste away.

Besides which they also taste the best.