After 3 miles, the oil in a diesel engine is as black as sin but it's still good.
It's down to the individual but I wouldn't bother.
An example is a 1997 R reg 528i E39 with over 200,000 miles. It had a problem where it wouldn't change up into 4th unless you used Steptronic. We tried everything including fitting a known good valve chest. The original 1997 oil was drained into a clean container and whilst pretty dark, was still clean enough when you had a bit on your fingers. It went back in, and no, the 'box was still misbehaving. In the end I did change the oil - no difference.
In the end, a faulty ABS ECU was causing the problem. Once replaced it was perfect.
I've done transmission oil changes on cars and whilst the owners swear blind it was different, they always felt the same to me.The gearbox, not the owner.
To each their own.