I've never heard that particular terminology ("fourth grade of C") either, but I'm guessing the rationale is this:
If you're harmonizing an F chord, normally the key of F major has a B-flat. However, since you're harmonizing an F chord in the key of C major, you will not use a B-flat, since B-flat is not in the key of C.
As such, this F major chord will not have a B-flat, but rather a B-natural, which is the #11. (Similarly, the maj7, E-natural, is in the key of C as well.)
It may be helpful here to note "the rule of seven": if a chord extension is higher than 7, just subtract 7 to get a quicker idea of what interval that extension is. For instance, if you have trouble remembering what an 11th above a pitch is, just think 11-7=4 to realize that an 11th is really just a 4th above. (Obviously there are some concerns here with octave displacement, but this is just a fast way to determine the pitch name [or pitch class, if you've heard that term].) Similarly, a 13th is just (13-7=6) a sixth above.