Screenshots produce low-quality images. Saving the image is a better option, and Downloading the image is the best way to get the highest resolution version available on SmugMug.
Instructions
When viewing a specific image you want to keep...
Save Image See the first image, below.
Computer: Right-click (CTRL+click for Mac), select "Save image as..."
Phone: Tap/press and hold on the image, select "Add to Photos" ("Save image" for Android)
Download Image See the second image, below.
Computer: Click the underlined down arrow; locate the image in your Downloads folder.
Phone: Click the underlined down arrow; locate the image in your FILES folder (you will NOT find it in your Photos folder if you use the Download method).