Virginia Woolf introduces Peter Walsh using Clarissa's memory.

The intelligent reader can immediately understand that the two characters had been in a good relationship, maybe a partnership. Indeed, Clarissa remembers exactly an episode happened years before and, above all, she perfectly remembers the little conversation they had.

 He was teasing her because she was contemplating the flowers outside. However she was able to face the joke; this makes the reader understand that they knew each other well.

They are still keeping in touch. This means that , even if they had not get marry ( Clarissa is called Mrs Dalloway, not Mrs Walsh) they had built a good relationship which is still continuing now.

Clarissa remembers a lot of him, even his expressions, as that one of the cabbages. Therefore, Peter Walsh was and is important for her.