From the point of view of the owner of The Tutoring Center, who is looking for potential franchisees, it's important to use the full name of the company (including the opening The) at every opportunity, as a matter of branding. So, to the extent that you are representing this owner, you are well advised to follow the recommendation of deadrat and restructure any sentences that would otherwise leave you with a double-article ("a The") juxtaposition.
Other people facing similar juxtapositions, however, do not have to bend over backward to retain the company's favored wording. For them, the simple solution is to drop the word The from the company name. Here is an example from a description of a geocaching challenge called "That ALGEBRA Cache":
The puzzle-phobic Duck phones several friends, purchases a Learning Company course called "Mathematics Made Simple (but not THAT Simple!)," and slips the CO a bribe. He completes his solution after 8 hrs and 6 bottles of Tylenol. Fortunately, the cache is only 22-1/2 miles away from his pond, "as the duck flies"--and a duck who's out to be First To Find can fly mighty fast!
The company's official name is, as you probably know, The Learning Company; but the author of this description is perfectly within his rights to use the wording "a Learning Company course called" instead of "a course from The Learning Company called..." Indeed, the Chicago Manual of Style, fifteenth edition (2003), goes a step further and recommends lowercasing the even in situations where it could be capitalized without resulting awkwardness:
INSTITUTIONS AND COMPANIES
8.73 When to capitalize. The full names of institutions and companies and of their departments, and sometimes their short forms, are capitalized. A the preceding a name, even when part of the official title, is lowercased in running text. ...
[Relevant Example:] the Hudson's Bay Company
This arrangement, of course, frees writers to drop the in favor of a whenever a sentence calls for it:
Pierre reached a Hudson's Bay Company outpost just as the snow began to fall heavily.