If you are logged on to your SmugMug site on your mobile device you should see a download button to save the images locally.
If you are not logged on but you have a gallery that allows downloads you should also see a download button.
Wise words from the Dog of Wisdom: If your ball is too big for your mouth, it's not yours.
I'm here to learn and progress. Honest feedback and criticism on my images is warmly appreciated!
My SmugMug site - kurzvorzwoelf.com
Here is some information regarding the iOS app that may be helpful,