EDIT - SOLUTION:
I ended up figuring out a way to solve this issue. Because manually changing the height of the ImageView removes the extra padding,
I ended up figuring out a way to solve this issue. Because manually changing the height of the ImageView removes the extra padding, I ended up finding the dimensions of the original image, and apply them to the ImageView once the ImageView dimensions can be calculated. Here is the final result:

This is the final working code:
AlertDialog.Builder builder = new AlertDialog.Builder(this);
builder.setPositiveButton("Get Pro", new DialogInterface.OnClickListener() {
@Override
public void onClick(DialogInterface dialog, int which) {
}
}).setNegativeButton("No thanks", new DialogInterface.OnClickListener() {
@Override
public void onClick(DialogInterface dialog, int which) {
}
});
final AlertDialog dialog = builder.create();
LayoutInflater inflater = getLayoutInflater();
View dialogLayout = inflater.inflate(R.layout.go_pro_dialog_layout, null);
dialog.setView(dialogLayout);
dialog.requestWindowFeature(Window.FEATURE_NO_TITLE);
dialog.show();
dialog.setOnShowListener(new DialogInterface.OnShowListener() {
@Override
public void onShow(DialogInterface d) {
ImageView image = (ImageView) dialog.findViewById(R.id.goProDialogImage);
Bitmap icon = BitmapFactory.decodeResource(context.getResources(),
R.drawable.whygoprodialogimage);
float imageWidthInPX = (float)image.getWidth();
LinearLayout.LayoutParams layoutParams = new LinearLayout.LayoutParams(Math.round(imageWidthInPX),
Math.round(imageWidthInPX * (float)icon.getHeight() / (float)icon.getWidth()));
image.setLayoutParams(layoutParams);
}
});
And the XML: