It's unfortunately true: the trap can be escaped from.
Let's start by assuming the opposite: that it's impossible to leave. The starting square, assuming the crab's doomed to wander the trap forever, must be visited an infinite number of times. That would then, using recursive logic, lead us to believe that all four squares surrounding it must also be landed on an infinite number of times, and the square surrounding THEM to be visited an infinite number of times, until finally we come to the edge pieces. And then we return with a contradiction:
How can you visit an edge piece an infinite number of times, travelling in all four directions as a result, and NOT leave the grid?
So, since we proceeded under the assumption that escaping is impossible, and the train of thought ended with the conclusion that you can escape, this must be false and so the trap must be possible to escape from.