En el ejemplo - A él no le importaba lo que yo hubiera dicho. He didn't care about what I had said. ¿Por qué 'hubiera dicho' y no 'había dicho?

Hola Peter,

Both "hubiera dicho" and "había dicho" would be grammatically correct. If you say "lo que yo había dicho", using the indicative mood, that'd mean literally "what I had said". If we use "lo que yo hubiera dicho", using the subjunctive mood, that'd mean "whatever I may have said". The second option with the subjunctive implies uncertainty, doubt, unknown information...

I hope this helps.

Gracias 

Inma