Is there a way to disable the Mighty Eagle icon?

Solution 1:

This web page explains how the Mighty Eagle works.

The salient points are:

• You will not receive any stars or points from using the Mighty Eagle - your performance is considered in relation to a completely separate 'Eagle Score'
• It's not a one-use item - once you purchase the Mighty Eagle you will have permanent access to it. However you can only use it once per hour on levels that you haven't beaten yet.

So you could purchase the Mighty Eagle and then use it (without receiving any points or stars and thus not cheating), and the icon would presumably not be available on that level, or any subsequent unlocked levels for the next hour.

Note - I haven't purchased it myself, but after reading about it there's a strong possibility I will!

Solution 2:

As of now with the current version (v 1.5.0), No, there doesn't appear to be any permanent way to remove the Mighty Eagle icon from ever showing.

From what I saw, it shows up after the 3rd or 4th replay of a level. If you click on the icon, and then close it with the X, it will disappear, but then it shows back up on the 3rd or 4th replay of the level. I tried running in airplane mode as well, with the same results. There don't appear to be any menu settings allowing it to be removed or moved to another area on the screen.