Is one absolved from sin for obsessive thoughts that arise years after mistakenly returning an extra jacket? And is it considered a lie for a mother to say "we were traveling" to explain being late?

Your obligation is fulfilled by rendering the trust and its acceptance by its owner. Seeking forgiveness and repentance are sufficient for the lie regarding the delay, and your mother should repent since the lie originated from her. Disregard intrusive thoughts so they do not lead you to dire consequences.