calories burned

If you want to lose weight, you need to have a calorie deficit. You can eat some of the exercise calories, but don't eat them all.

i eat enough back to keep over 1200 net calories per day, but not all of them

I try to stay with the alloted amount of calories, but it is very nice to have some calories 'banked' through exercise on those days you happen to splurge a little. So...both your statements are correct; you can lose more quickly if you don't eat your extra exercise calories, but you should lose at the same rate you originally set as your goal even if you do.