Those are Hotmail "placeholder" images.
Unfortunately Hotmail does not tell the app that "there is an image, but it's a placeholder", and so AquaMail shows those, not knowing that they're really "images that mean an absence of an image".
The only way to change those is in Hotmail:
1. Log in your account at https://profile.live.com.
2. On the left hand side, click Change picture.
3. Click Browse... then choose the picture from your computer.
4. Wait for it to load then click Save.
After you've made the change there, please long press an account in AquaMail (on the app's main screen) -> account setup -> Next.
This will clear the app's "cache" and it will fetch the updated image on next mail check.
Without the "account setup" step, AquaMail does this every 24 hours while checking mail.