A very basic question about calories

Firstly MFP isn't a TDEE site - it completely removes exercise from your base calorie goal. Be very cautious about comparing numbers using two different methods. (Although if your only exercise is 30mins of walking then that difference is small.)

It also doesn't set your calorie goal, let alone automatically, that's set by your current stats (out of your control), your activity level (within your control) and the rate of loss you choose (very much your choice).

And it's choosing a fast rate of loss that is driving your daily allowance down to 1235 + exercise calories.
If you don't want a tiny calorie allowance then....

• Don't pick a rapid rate of loss.
• Raise your activity level.
• Do more exercise.

If you don't want to eat under your BMR then you need to accept a slower rate of loss or take steps to make the difference between your BMR and TDEE much wider - that's down to activity and exercise.

BTW - not eating under your BMR is a guideline, your body doesn't know what your BMR is and doesn't shutdown if you go below it. But there may be consequences in under-eating for a prolonged period of time.
In many ways it's quite a sensible guideline though.

It's not really appropriate for people to decide your calorie level as you need to have a serious think about what calorie level is sustainable for the long haul of losing almost 100lbs. Adherence is far more important than speed IMHO unless you have a medical imperative to lose quickly.

Yep, as others have noted ....

BMR is not relevant here. TDEE is what matters. Yours is 2260, so if you told MFP you want to lose 2 lbs per week, it's subtracting 1000 calories per day from that 2260, because 1000 x 7 (days in the week) = 7000 = 2 lbs of fat.

In theory, it's that simple - just eat your 1235 calories per day and you will lose 2 lbs per week. In practice, 1235 is not a lot of food and you're probably better off taking it slower than that. I would, personally, start with 1735 to lose 1 lb per week and see how it goes for a while. If you find that a comfortable caloric level, then presto, rinse and repeat for, well, a pretty long time. If you find you can handle the 1735 and want to push things a bit faster, you can adjust the calories in a month, or at any point. My point being, you're more likely to get yourself on a good, solid sustainable path if you don't deprive yourself too much. It's a marathon, not a sprint. In this particular kind of race, sprinters end up at the side of the road, out of the race. A moderate, steady pace works much better. The vast, vast, VAST majority of people who lost the kind of weight you want to lose did it slowly and surely, being careful not to deprive themselves or overdo things with the calorie restriction and tbh for most people 1235 is either overdoing it or very close to overdoing it as far as dieting for more than a couple/few weeks is concerned.

As @KrissCanDoThis noted, be sure to eat back your calories from any workouts.