répondrait is progressive past → "was answering". And répondre au téléphone is an expression that translates as "to answer the telephone":
'Would' doesn't mean quite the same thing as 'was doing', but I agree I'm just as confused as you.
'The girl would answer the telephone' means she would answer the telephone in certain a circumstance or a particular time, 'The girl was answering the telephone' means she was answering the telephone at a particular time or in a particular circumstance (in the past).
I don't know how to put it clearer. I only speak English but have had limited formal schooling and have no idea what 'past perfect'/'past imperfect', or any of the more technical grammar terms mean. I wish this was explained in clearer terms.