Arya knew she couldn't fight the man on this and why not, being his temporary companion might prove useful. The man wasn't on her death list but most of his family was including his sister. Although she had no idea of the true relationship between the siblings. Maybe the man knew where they were and could still be useful in other ways of letting those details slip.
"Yes, my lord," she agreed gruffly and let go of her sword to stay put in its sheath. She walked towards the road with the man, staying behind him only slightly.