Sorry for taking so long to respond, I was having issues accessing this account again.

This happens with every single picture that I've received on my new phone, even when I send myself a picture.

When I got my new phone, my old texts had been transferred from my old Samsung Galaxy S3 to my new Moto X 2014. I went back and found a text from September 28, which was the last day I had my old phone (I upgraded September 29th). All pictures pre Sept. 29 were perfectly clear. All texts post Sept. 29 are blurry. Here are examples of similar pictures sent to me both before and after the upgrade.

Before:

http://i.imgur.com/JFvFbxG.png

After:

http://i.imgur.com/RfHkSsF.png