I have received a similar notice before... they are common and I wouldn't fret. The IRS makes mistakes ALL THE TIME! I am a CPA and work for a business and see it often.
My advice, gather all your documentation then write a straightforward cover letter to support it. At the very top of the letter reference the document number.
Follow this basic outline:
1. In your letter to me dated XXXX, the IRS asserts that I improperly took the Lifetime Learning Credit. (Then, don't get argumentative saying, "You are wrong because blah blah blah..."
2. Move on quickly to cite the IRS rule applying to your situation in exact words: "The IRS Code XXXX relating to the Lifetime Learning Credit imposes these eligibility requirements...."
3. "I assert that I am entitled to the Lifetime Learning Credit because I meet the eligibility requirements of IRS RULE XXX as follows:" Attach copies of your documentation, establishing each point. If certain points require explanation -- such as the fact that the education need not be work related feel free to provide brief narrative.
4. "Please review this information and respond at your earliest convenience" and then provide your contact information.
Make sure you're throwing their own rules back in their face... so reference the rules on the IRS website:
http://www.irs.gov/publications/p970/ch03.html#en_US_2013_publink1000178154They will most likely go away. If they don't and you're being harassed (highly unlikely) hire a CPA.
These letters are issued when something gets flagged in the computer system that raises a question. At this point, there has been very little human judgment involved. When a human gets involved it is likely to go away quickly.
The business I work for was just randomly audited. They went away quickly and I have found that they often do if you just get your facts together and respond calmly and clearly.