This question comes down to concision - saying the thing we want to say clearly in as few words as possible.

We'll start with a good concision rule: whenever possible, we want to use our subject only once. We can eliminate A and D for using both "whales" and "they".

Let's look at the remaining answers:

B. Last year, fewer whales than there ever were before traveled back to their tropical breeding grounds in search of warmer water.

This sounds okay, but it's the longest answer. We should be suspicious.

C. Last year, fewer than ever before, whales traveled back to their tropical breeding grounds in search of warmer water.

This is much shorter, but it doesn't actually make sense. The commas now set off the phrase "fewer than ever before", indicating that it is extra information ... but it isn't. It's pretty important to the meaning of our sentence! Without it, we just have "Last year, whales traveled back to their tropical breeding grounds in search of warmer water". We miss the entire point: that there aren't as many whales as before. Eliminate C.

E. Last year, fewer whales than ever before traveled back to their tropical breeding grounds in search of warmer water.

This is the same as B, just without the words "there" and "were". Does losing those words change the meaning of the sentence? Nope. Does it make the sentence ungrammatical? Nope. On the GMAT, if two answers say the same thing and the shorter answer is grammatical, we should always pick the shorter answer. So we can pick E.

Note: if you're trapped on a Sentence Correction problem like this one, it's often a good idea to go with the shortest answer because it's the most concise. In this case, that would be E, the correct answer!