Logitech *should* do a replacement from what I've heard.
Dear Valued Customer,
Thank you for contacting Logitech Customer Care.
I see that you have sent us an email on 10/10/2010. I apologize for the delay in getting back to you, and thank you for your patience. I am sorry to hear that the screen on your Harmony remote is damaged, and I can certainly look into this for you.
Unfortunately, this type of damage is not covered under the hardware warranty for your remote. Also, Logitech does not offer any repair services for Harmony products at this time. I am sorry for the inconvenience.
Thank you once again for contacting Logitech Customer Care.
Regards,
Duncan
Logitech Customer Care