exercise calories confusion

Simply put, you can eat back the 300 calorie and still lose weight (a gross of 1980 - nett of 1680)

Yup, you can eat them back if you want. Depending on the day that I have I either end up eating them all back or around half. Just play it by ear and if you are hungry and have the extra calories then eat them as long as they are healthy calories : )

BMR is the level required for just being alive. If you were in a coma, you would burn BMR. Do you mean your TDEE is 1980? Whether you eat the calories back or not depends on how you determined your calorie goal. If you used the MFP method (NEAT), then no exercise is assumed, and the calorie goal given to you includes a deficit. If you burn additional calories through exercise, you are expected to eat them back to prevent you deficit from growing too large (there are a host of reasons you want a small deficit, including minimizing muscle loss and ensuring you get all necessary nutrients). If, however, you used the TDEE method and accounted for your exercise in your weekly goal, you would not eat extra. I use the TDEE method and assumed 3 one hour weight lifting sessions a day, so I don't eat extra on days when I lift. I did not factor in any runs, however, so when I run on top of my weight lifting, I do eat extra calories for the runs.

Make it easy for yourself. Forget about BMR and TDEE.

Tell MFP how much weight you want to lose per week. How much you should try to lose depends on how much you have to lose. Use this as a guide:

75+ to lose = 2lbs 
50-75 to lose = 1.5-2lbs 
25-50 to lose = 1-1.5lbs 
15-25 to lose = 1lbs 
0-15 to lose = 0.5lbs

MFP will then give you a calorie goal with no exercise factored in. This is the goal you want to reach, not come in under. If you exercise, you will need to eat more in order to "net" this goal, which is why your green "goal" number goes up. So eat your exercise cals (or 1/2 of them or some other proportion of them if you think, as many do, that MFP is overestimating calorie burn).

Hope that helps. It doesn't have to be complicated.

In theory, you can eat back exercise calories and still lose weight. However, you should be aware that the majority of calculations for the majority of people will be overestimated, so you may struggle if you eat back all exercise cals.