You have to use the hook_field_widget_form_alter function and inside there look for the variable details using dpm() and then alter the button using an attribute from the Forms API.
But I would suggest to make the widget field read only on the edit form and not remove the delete button.
// Hide remove button from an image field
function MYMODULE_field_widget_form_alter(&$element, &$form_state, $context) {
// If this is an image field type
if ($context['field']['field_name'] == 'MY_FIELD_NAME') {
// Loop through the element children (there will always be at least one).
foreach (element_children($element) as $key => $child) {
// Add the new process function to the element
$element[$key]['#process'][] = 'MYMODULE_image_field_widget_process';
}
}
}
function MYMODULE_image_field_widget_process($element, &$form_state, $form) {
//dpm($element);
// Hide the remove button
$element['remove_button']['#type'] = 'hidden';
// Return the altered element
return $element;
}
Useful issues: