Should I eat back work out calories?

Were the 1000 calories from you typing X minutes of walking into the MFP exercise database to log it, or was it the all-day calorie adjustment from your synched fitness tracker, or something else?

If it's the calorie adjustment from your fitness tracker, it includes calories to adjust between how much MFP thought you would burn based on your MFP profile settings, and what the tracker thought you burned from "watching" what you did all day long. It wouldn't be just the walking, it would include your job, home chores, etc.

If it was from the exercise database, that does tend to overestimate walking. If you know the approximate speed and time you walked, this will give better walking calorie estimates:

https://exrx.net/Calculators/WalkRunMETs

Set the energy box to "net".

If you follow a consistent routine for about a month - a whole menstrual cycle if that applies - you'll be able to look at your weight loss rate and use that to adjust how fast you're losing weight - to get it happening not too fast, not too slow. By "consistent routine", I mean hitting close to your calorie goal most days (on average), and eating back about the same consistent proportion of your exercise calories (50% or 75% or whatever). If you're not consistent - like eat them sometimes, other times don't at all - it's harder to know how much to adjust.