earned workout calories

of course you will lose faster by sticking to your regular calories, but you'll also get hungrier a LOT faster (not to mention, hit a plateau faster usually)

I personally would recommend to eat back at least some of the calories exercised. this way, you can get used to slowly lessening how much you eat rather than suddenly doing so. you will get used to a smaller amount of food gradually this way.

Is it better to eat the calories you earn during the day from working out or to stick with your regular calories? Which way will you lose weight faster?

When you entered your stats into MFP when you started, it figured a calorie deficit into your daily calories that will allow you to lose weight at the rate you entered. If you do any exercise, those are additional deficit calories, so you should eat those back.

For example, I'm a lightly active woman looking to lose 1 pound a week. That means MFP calculated a NET of 1,400 calories. When I don't exercise, I eat 1,400 calories. When I do, I eat 1,400 + my exercise calories burned - and I still net 1,400.

By doing this, I'm losing 1 pound a week consistently because the calorie deficit it already built into my net calories.