Responses to these sorts of questions are some of the most annoying things EVER. I feel similarly to all the "how to prevent stretch marks crap". You simply cannot "fill" bat wings unless you got super muscly.And I'm TALKING SUPER MUSCLY!!!!
They will either slowly shrink up with time (can take up to three years) or it will not.
Yes, diet, "CAN" inhibit the body from doing it's thing in shrinking up skin if you are malnourished , but gosh darn it people, STOP saying you can do this or this or this to get rid of loose skin!
Maybe you want to have hope that your skin will bounce back hearing these wive's tales helps, but by saying if you do this it will, you are basically thumbing your nose at everyone who does THAT and still has loose skin.
It's a lot genetic, age, and perhaps length of time you were overweight.
Tell to this person's face that if they ate right, or lost weight right, or toned right, they wouldn't have loose skin, OK?
Ok, that's not arms. Here are arms. Which aren't mine when I lost weight, but could have been... And I "lost" right. I "exercised" right. I lifted heavy and guess what, my arms and muscles were strong and toned and SHOWED (A personal trainer was might impressed with my triceps especially) and I had major bat wings.
So, the answer is, truly, time will tell - time and a healthy diet. Strength training is good for you, so do that, but don't do it expecting to get toned arms with no bat wings. And IF your bat wings slowly disappear with strength training - it wasn't the strength training. It was TIME.