how many calories do I eat back from exercise?

Well if your goal is to eat 1300 calories a day and that goal is based on the idea that if you eat a certain amount below your BMR+daily activity then you should eat back all of your exercise calories.

The point of exercise isn't to burn calories its to get healthier, fitter and maintain your muscle during diet.

The only trick is it can be difficult to get an accurate read on how much you have actually burned from exercise especially given a lot of gym equipment or calculators will overestimate the amount you burn. For that reason many recommend eating back half of the calories you think you burned.

Personally I just go for a low estimate on my burn and eat it all back.

I aim for 1800 calories a day because I think on average just being myself and moving about I burn 2400 calories and a 600 cal deficit is what I am aiming for. As a result if I do intense cardio for 1 hour I log that as 400 calories and I eat 400 calories more that day.

If you have a very regular workout schedule you can just average that exercise out for the week and add it to your goal of 1300 and just eat that every day and not worry about how much you exercised on one day compared to another.

It all depends on how you get your exercise numbers, any way you get them they are all estimates and are never going to be 100%. I always aim for 60-70% of what I burn just to allow for an overestimate.

None. Your weekly TDEE should already have all activity including formal excercise taken into account.

If her goal calories is 1300 then she isn't using TDEE and isn't including exercise into her calculation. If you just read the number MFP suggests and don't use MFP to enter your exercise you would just eat 1300 every day regardless which is wrong. I think she is asking if she should eat back her exercise calories and the answer is yes. The difficulty is just in accurately addressing your calorie burn from exercise.

Basically if you exercise routinuely you want to find out how many calories it requires for you to be at maintenance which would include all that calorie burn from exercise (your TDEE) and then for weight loss you'd want to eat approximately 20% less than that value. So if your TDEE was 2000 you'd eat 1600.

The trick is figuring out how many calories puts you at maintenance with your current exercise level and that is up to you to determine.