Extra calories added after exercise

Yep.
MFP gives you a calorie goal based on what you would burn WITHOUT EXERCISE. This is so you lose at your selected rate even when you don't workout.

If you workout your daily calorie burn increases. To maintain the same deficit and to keep your deficit reasonable you should eat some of your exercise calories back.

Example:

Before exercise burn - 1800
Lose 1 lb per week - -500
Goal WITHOUT exercise - 1300

Exercise burn 400 calories
1800 + 400 = 2200
Total burn for day - 2200
Lose 1 lb per week - -500
Goal WITH exercise - 1700 or NET 1300

You will still lose weight if you don't eat them, but you will probably feel a bit hungry and may burn out quicker (I know eating so little + working out makes me hangry and sick of dieting). I agree with what TeaBea said, that if you log a workout and MFP says you burned 500 cals, then only eat back about 200-300 of that. It is most likely overestimated.

I have found that my fitbit is quite accurate, though. I feel comfortable eating all of those calories back.

I also don't log weightlifing as burning any calories. But I do eat back whatever fitbit steps I take during my weightlifting sessions.

It really depends on your exercise and your average heart rate, current weight and height and general activity level. How hard are your exercising and how many times a week? Do you also walk a lot during the day?

I eat back 35%-40% of my exercise calories and I still manage to lose about a pound a week. I am 27,5'4.5, 142.4 pounds and workout 6-7 times a week ( sometimes twice a day). If I only eat 1,450 calories a day as MFP is suggesting ( without exercise) and exclude the calories burned during exercise ( I use a great heart rate monitor to get a semi accurate number of calories burned) I feel like I am starving and I end up bingeing. On days I workout once a day ( and burn around 500 calories) and walk over 6,000 steps I consume around 1,650-1,700 calories. On days I workout twice a day and walk over 6,000 steps I eat around 1,850-1,950 calories. On days I don't workout and only walk around 12,000 steps I eat around 1,600 calories. I made the decision to loose weight slowly and keep my sanity, while still training hard.