Is Debería also correct?

Hola Shirley

It's using "wouldn't" in the English because it's the most natural way to translate what we are saying in Spanish. The literal translation would be "They didn't let her through" (past tense). I can't really see the lesson as you're tagging a lesson about the subjunctive, but the answer is you can't use "debería" here - debería means "should". If you followed the literal translation using "would" you could conjugate the verb dejar in the conditional, so:

Ellos no la dejarían pasar. 

I hope this clarified it.

Saludos

Inma