Okay, let's start from the beginning.
Disk Utility is saying the .dmg is in the trash. If you empty the trash, then look in the trash, is the dmg still there? You won't be able to empty the trash if the file is in use. If the .dmg is mounted on your desktop, it's in use and emptying the trash won't make it go away.
Why is it appearing? Because way back when you installed Evernote, you downloaded the .dmg, you mounted the .dmg on your desktop, and then you double-clicked Evernote from the .dmg. That's not what you're supposed to do. You're supposed to copy it to your applications folder and then double click it in the applications folder, never from the .dmg. By double-clicking from the .dmg, you told your computer, "do not make this program live in my applications folder. make it live in this .dmg file. Every time I use this program, automatically mount the .dmg and run the application."
Generally speaking, unless you have a clear reason to do otherwise, you shouldn't double-click anything in a .dmg.
Okay, moving on. Why is the .dmg popping up every time you print?
Evernote has a feature that lets you save a note by using the Print command in a program, and choosing "Print to Evernote." Whatever is in that window becomes a note.
So, here's what happened. You double-clicked the Evernote icon inside the DMG. That told your computer, "Evernote lives inside this DMG. Automatically mount the DMG when I want to use Evernote."
Every time you use the Print command, your computer says "Oh, print to Evernote is installed! I need to start Evernote. Okay, I have been told to mount this DMG and run Evernote from the DMG whenever I need to use Evernote. Okay, now mounting DMG...
To stop this from happening, you must do two things.
1. Remove Print to Evernote.
2. Delete the DMG.
1. Open the Library folder inside your Home folder. (Note: there are actually two Library folders. You do not want the one that lives on the top level of your hard drive. You want the one that lives inside your Home folder.)
If you're using OS X 10.7 ("Lion") or later, this folder is hidden. To get to it on Lion or later, click on the Go menu in the Finder, choose the Go To Folder command, and type
~/Library
Once you are there, look for a folder called PDF Services. Open it and look for Evernote. Move it to the trash. That will stop Evernote from running every time you use the Print command.
2. Make sure the DMG file is not mounted on your Desktop (you can restart the computer to be sure), then choose Empty Trash.
