换一种说法希望你能看明白：
The teacher didn't blame what he had done last friday.这句话肯定是对的,因为what 引导的是一个宾语从句.句子结构是:主+谓+宾从,这里的宾语和谓语产生了逻辑关系,所以从句一定要遵循时态规则的,即,what he had done 是过去的过去,要用完成时.
再看看原句：The teacher didn't blame him for what he did last friday.
句子结构：主+谓+宾+宾补 这句话中 for 引导的原因状语作him的宾语足语,跟宾语him是并列的,并不跟谓语产生逻辑关系,跟谓语产生逻辑关系的只有him,for引导的宾主补足语只是补充说明他上周五做的事情.
所以应该用did,过去式.