Do I have to pay fees in excess of legal retainer if not authorized?

Signed agreement to perform legal research for $2500 retainer, determined by "nature and scope" of question, with contract detailing return of remainder at conclusion. Research was done (by phone/email), but answer returned was incorrect! And now, received a non-itemized invoice for additional $2000 in fees above the (paid) retainer. The additional fees were never discussed/authorized. Feel like lawyer educated himself (poorly) at my expense. Do I have recourse?