My clients offer was rejected, how do I update the Referral Manager to reflect this?

Since you've made an offer, it will benefit you - in terms of the algorithm and your rankings - to keep the client at the 'We Made an Offer' status. Simply update the status as 'Offer' with the offer sub-status as 'Offer Was Rejected" 

Offer rejected

Moving forward, you'll just want to continue selecting 'No Offers Outstanding" until your client finds the next property on which they would like to make an offer.

offer no offers outstanding