Q: Lexus is250 2006 electronic power steering problem

It is unlikely the battery terminal connection is a cause of the fault you are describing. If they have actual evidence of a fault related to the "connection", they should have provided that information to you. If no evidence is provided, they are obligated to refund your money as you were obviously given a useless, indeed incorrect, diagnosis. The problem you are describing is probably electrical in nature and looking through the NHTSA database, I see a non negligible number of like complaints from other owners (same year, make, model) so you are not "alone". When this new type of "electronic" steering system first saw widespread use, there were occasionally problems due to design glitches and unforeseen operating issues. Of relevance, in 2009, there was a Lexus Service Campaign (designated by Lexus as CSC-10028182-9096) to address hard steering in your year, make and model. The electric power steering link assembly was the problematic part and Lexus, at that time, was replacing the component for IS250 customers at no charge. An initial thing to check is whether your VIN number was included in that special service campaign and, if so, whether the repair was performed. If the service campaign is not relevant (or the repair has already been implemented on your car), what you will need to get your issue resolved is an electronic power steering system diagnostic during which a certified Mechanic, dispatched by YourMechanic right to your location, will perform the necessary tests to identify the root cause of the failure. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.