Let’s begin from the correct answer. Understanding why D is correct greatly helped me understand why the others are incorrect.
D. A 2013 agreement among North American governments reduced the quantity of tomatoes that Mexican producers are allowed to sell at below-market prices in the United States. Reduced is correct for an action that happened in 2013.
Are is correct for an agreement that is still in effect.
The agreement reduced the quantity in 2013, and this agreement still identifies the quantity. That’s the exact meaning the sentence conveys.
A. A 2013 agreement among North American governments reduced the quantity of tomatoes that Mexican producers had been allowed to sell at below-market prices in the United States.If I say –
When I came to the park I noticed that a young lady had smiled at me, then something must be wrong with me. Otherwise how to explain that I noticed something that happened even before I came to the park. That’s nonsense. Similarly, if we say that:
A 2013 agreement reduced the quantity that Mexican producers had been allowedThen we mean that a 2013 agreement reduced something that happened before 2013. These two actions are in different timeframes. For example, when I say
I want to stop World War II, then anyone understands that it is illogical because I am too too late to do that.
B. A 2013 agreement among North American governments
reduces the quantity of tomatoes allowed for sale
by Mexican producers at below-market prices in the United States.
A 2013 agreement reduces... I tend to think that
reduced would match here better because the agreement reduced the quantity when it came into force in 2013. Additionally,
...allowed for sale by Mexican producers... changes the meaning of the original sentence because Mexican producers didn’t allow, but instead they were allowed by whoever.
C. A 2013 agreement among North American governments reduced the
tomato quantities that Mexican producers
had been selling at below-market prices in the United States.
We usually don’t say
tomato quantities, but say
the quantity of tomatoes.
...Mexican producers had been selling... again leads to illogical timeframe mismatch.
E. A 2013 agreement among North American governments reduces the tomato quantities Mexican producers have been allowed to sell at below-market prices in the United States. A 2013 agreement reduces... the same problem as in B is repeated.
...the tomato quantities... the same problem as in C is repeated.
...Mexican producers have been allowed... we are talking about a general rule which is still in effect, thus we need Present Simple.
Hence
D