Why does Marquette University offer a course on J.R.R. Tolkien?

Because he's popular, of course, but also because they have the manuscripts:

Marquette is one of the main repositories of Tolkien's drafts, drawings and other writings _ more than 11,000 pages. It has the manuscripts for "The Lord of the Rings" and "The Hobbit," as well as his lesser-known "Farmer Giles of Ham" and his children's book "Mr. Bliss."...

... Marquette students [study] Tolkien's revisions, notes, detailed calendars, maps and watercolors on site at the school's archive....

"One of the things we wanted to impress upon the students was the fact that Tolkien was a fanatical reviser," said [the school's archivist Bill Fliss]. "He never really did anything once and was finished with it."

Why does Marquette have the manuscripts?

Marquette was the first institution to ask Tolkien for the manuscripts in 1956 and paid him about $5,000.