Code P0741 for the diagnostic for Toyota Corolla 2006 = Check engine light came on. 129,000 miles

Just take car to AutoZone to use their Diagnostic Code Reader and then they can look it up and tell you what is wrong and part that you should replace.

Time for a rebuild

Very few transaxles see much over 100,000

Check this link out. P0741 OBD II Trouble Code

Yeah Toyota is aware of this situation.Production changes have occurred to correct this condition.
You did the right thing to take it to the the dealership because when they pulled the code p0741 they had to apply the Toyota Technical Service bulletin TC008-04" to your vehicle.
They had to perform several tests and since you said they replaced the ECU for free it was because your vehicle was lower then 5 years old and less then 60,000 miles. This TBS is covered by the powertrain Warranty. They had to replaced the ECU with an updated unit, and that particular warranty is in effect for 96 months or 80,000 miles. Your car should be back on the road running like a champion and you should NOT have the same code again.

it means that either your solenoid is getting stuck or not performing well and getting stuck .check also for lose conections on the solenoid if not replace tha sensor

http://www.toyotanation.com/forum/showthread.php?t=236000

P0741 deals with internal transmission torque converter slip. A proper scan tool that is capable of reading the sensor's data inside the transmission would show the slipping torque converter and the fluid temperature.
It is critical to know exactly what conditions are present when the code stores. If the codes were not erased, they could be old codes in it's history.
Go back to the transmission shop or where you had the work done on replacing the TCC solenoid and have them read and clear the codes history. As mentioned, they could be old codes that is being read prior to your repairs.
Thank you for using Fixya and good luck, Have a shop verify line pressure, and provided no valves in the TCC hydraulic circuit are worn, replace the torque converter. Also, Lubegard Shudder Fix will at least fix this for awhile. Or try a transmission flush by a shop that uses BG brand products.

firstly it could be that the check engine light is mal-functioning or not. why not drive it as they said and if after that its still on get back to us.

code PO 741 torque converter clutch,circuit performance problem or stuck in Off position

This fix comes from the service manager of a Toyota dealer, he is a online expert named Toyota Ed.

Toyota is aware of this situation. Production changes have ocurred to correct this condition.

Here is what you do: Take your vehicle to your Toyota dealer. Tell them that you have a P-0741 code, and you want them to apply "Toyota Technical Service bulletin TC008-04" to your vehicle. They will perform several tests, and if you vehicle is lower than 5 years old, and less than 60, 000 miles, they will fix it for free. This TSB is covered by the Powertrain Warranty. Additionally, Thay may replace the ECU with an updated unit, and that particular warranty is in effect for 96 months or 80,000 miles.

This will definatly cure your issue