How to architect ConvNet to ignore top half of image
You could be right that ignoring top part of image would benefit the CNN. However, there is very little point in trying to architect this - if your premise that the CNN will ignore irrelevant details in the top half is correct, then that will occur anyway and there is no standard NN architecture that will help that other than disconnecting the top half of network, which is going to be logically exactly the same as programmatically slicing the image, with the disadvantage of storing and calculating with twice as many parameters.

You should either programatically cut the image in half or do nothing to the image and rely on the CNN's inherent ability to give low weights to irrelevant details. If you do the latter, you may be able to get around the learning of incorrect details in the top half by augmenting your data - e.g. add some noise to images*, especially in the irrelevant top half. Perhaps horizontally flipping a few images (and reverse relevant targets for the control class) might be another useful augmentation. Some augmentations could also be useful if you just take the lower half of the image.

* Noise should be something close to variations that could be seen when in use. E.g. slurring pixels left or right might be reasonable. Inserting "static" probably is not.