Contextual menu for files.
I don't know about you, but this annoyed me greatly, so I researched how to get rid of it. Why? With too much frequency, I'd accidentally pick the wrong one and then have to fix the mistake. I delete a lot more files than I move to Dropbox, so the Dropbox entry had to go.
From my research, here's the procedure I found. (Read all the way to the end of this how-to before you start.)
1. Navigate to the OS X /Library and then to the folder DropBoxHelperTools and delete the file DropboxHelperinstaller.
Next, before moving on, I want to explain an OS X command I'm going to refer to next called “Show Package Contents.” It appears in your contextual menu (right click) for an OS X app.
Background. An OS X app is actually a OS X folder. (A Unix directory.) Inside the folder is the graphic for the icon so that OS X can display the app to you in the Applications folder. Also in the folder is the executable code so that when you double click the app, OS X can find the binary code and launch the app. When you say, “Show Package Contents,” you're asking OS X to reveal the contents of the app's folder. You can then navigate in with the Finder and inspect the many files that comprise an app.
With that in mind, we can continue.
2. Navigate to and select the Dropbox app in /Applications.
3. Right-click on the app and select “Show Package Contents.”
4. Open the Contents folder.
5. Open the Resources folder.
5. Delete the file DropboxHelperinstaller.tgz
6. Restart the Finder. If you're not sure how to do that, see “4 Ways to Restart the Mac Finder.“
Here's another tip. When I do things like this, I create a holding folder on my desktop and actually move the unwanted files there. That way, if I need them again, they're easy to find. When all's well, I delete the holding folder (or maybe archive it).
Some experts have a personal protocol for renaming files they want to take out of operation, so that they're not active on a relaunch of the OS or app, but I like keeping the name of the deleted file intact.
After you restart the Finder, that contextual menu item for files “Move to Dropbox” will be gone.