Credit card charge that was not authorized

I recently had a credit card charge of 29.95 which was not authorized.  I contacted ANC Archives to refund and cancel the supposed subscription -- the firm stated it would cancel but would not refund because it was past the firms 7 day time frame.  It was billed on Dec, 31, 2015 ( which I just received today January 26th) this firm needs to be investigated.  George Phipps