How many miles do I need to walk per day to lose weight?

I started gaining weight because my thyroid was whacky, but now that I’m getting it under control with meds, I’d like to know how many miles per day I would need to walk on my treadmill to lose weight and at what speed I should be walking.

Before my meds, I was averaging 2.7 miles a day, with one day of rest, at about 2.9–3.3mph, with an average calorie burn of about 250–330. (I have a rib injury, so I can’t do really intensive exercises, otherwise I would be. Right now, walking and swimming are pretty much my only options.)

Before the meds, a combination of swimming and walking was getting me nowhere with weight loss (and should have been, especially with the amount of swimming I was doing during the summer), so now I’m hoping that I can actually make some progress. But I don’t know the ideal targets to shoot for for safe weight loss (1–2 pounds per week).

I don’t have a bad diet. I eat lean meat only, veggies, fruits, whole grains, etc. I don’t consume very much cheese, I don’t drink pop or alcohol (only a couple of times a year), or anything like that.

Being hypo, I know that some people have to work even harder than “normal” people to lose weight, even medicated.

Can anyone help me out?