There is an feature in outlook which should get the spellcheck to ignore original message text in reply or forward. Which can be found if you press the File -> Option ->Mail
You would believe that when you check the checkbox it should work.
However it’s not that simple. There is a big chance that you will still experience that it infect does check the original text.
In my case the function only work if I had the “Mark grammar as you type” checked and “Check grammar with spelling” unchecked. as displayed below
When I checked my friend Google a lot of users are struggling with this on several outlook versions. I have only tested it on the 2010 32bit version but give it a try and please comment if it helps you with another version.