Override Module for mobile users
I can think of two approaches.

The quick(er) dirty way:  

Hide it with CSS!

Problems:


I assume you're using seven or some other admin theme that you can't edit so all this will need to go in a module with drupal_add_js() or some other method for inserting JS.
After we determine if the visitor is on a touch device, we can't hide the element with simple jQuery because the element is dynamically inserted.


First, we'll need a way for JS to add CSS to the page. This function will let us do that:

function addCss(cssCode) {
  var styleElement = document.createElement("style");
  styleElement.type = "text/css";
  if (styleElement.styleSheet) {
    styleElement.styleSheet.cssText = cssCode;
  } else {
    styleElement.appendChild(document.createTextNode(cssCode));
  }
  document.getElementsByTagName("head")[0].appendChild(styleElement);
}


Then determine if the current visitor is on a touch device:

var is_touch_device = 'ontouchstart' in document.documentElement;


If so, add some CSS to page that hides the "Crop" button.

if (is_touch_device) {
  addCss('.manualcrop-style-button-holder {display: none;}');
}


The harder way:
Somehow determine if the current visitor is on a touch device via PHP. I don't have a foolproof method for this, but you can look into something like php-mobile-detect.

If you can determine that the visitor is on a touch device in PHP, you can return the manualcrop_croptool_process() function early. (Line 151 of manualcrop.helpers.inc). Of course, that will require filing an issue with module maintainer and providing a patch of those changes.