I have a 2003 Corolla/Automatic/280,000km/ with a transmission that causes a hard jolt every time I put it into reverse after a cold start. It only happens under those conditions. It has been getting stronger over the last few months. Once the car is warmed up after 10 minutes of driving it will go into reverse smoothly. When driving it shifts up and down fine.

There are no codes and I am the original owner and I’ve changed the fluid according to the owners manual interval. The last change was done about 20,000km ago.

Is my transmission failing? Is there anything DIY I can check or do? Right now I’m trying to avoid using reverse. I need new struts but I won’t bother with those if my transmission is imminently going to fail. 

Thanks for the help!