I'm not 100% sure what eating back calories is.
I assume it's eating extra to compensate for calories burnt during exercise. No. Not deliberately. I always make sure that I don't exercise feeling hungry so that my body burns fuel not muscle. I always eat protein after weights so that my body has something to rebuild muscles with.
I don't eat extra just because I exercise - our bodies weren't made to be sedentary so they don't need extra fuel to exercise unless you are an elite athlete.

I'm not big on calorie counting - I work on a principle of 5 meals a day.