Agreement are made between friends are made without an intention
A social agreement are made between friends are made without an intention of being enforceable. Where the contract is of a social nature, the law is assumed that the both parties did not indent their agreement legally binding. The majority of social and domestic agreements are not considered to be serious sufficient to influence the court that the agreement was always intended to be binding at the time.  While the most social agreements are intended to give rise to legal obligations, agreements to participate in a competition have been held to be enforceable. 
In case, Trevey v Grubb (1982) 44 ALR 20 where a Tattslotto entry coupon lodged by the one person on behalf of the m three member of syndicate won the prize. The high court held that it is an enforceable contract each party would have share the winning prize in the same proportion of cost have contribute to purchasing the lottery ticket. 
In Simkins v pays  1 WLR 975 the court held that a lottery ticket holder had to share his winnings with two other people who had regularly contributed. But they were not contributing on every occasion to the purchase of a group-owned ticket  .
So , both cases are binding the social agreements and the court give a decision of appellant was entitle to receive some percentage of money,
Application of Facts
According to the both cases, Trevey v Grubb (1982) 44 ALR 20 and Simkins v pays  1 WLR 975, who purchased the lottery ticket on behalf of the other group member is to share the winning amount of money with the all group member who are bounded in social agreement. In case of Harry and sally, they have mutual understanding if any of them or either Harry or sally buys the ticket both are entitle to share the wining prize of money. Applying both cases specially Trevey v Grubb; sally is binding the law of contract under the social and domestic agreement.
In this case, Sally is incorrect. They have mutual understanding about the social agreement. The amount of money winning in a lottery sally y obliged to with Harry. Otherwise Harry can take legal action to sally under the breach of contract.
A legal issue in this case is an offer and invitation of treat under the contract law.
An offer is a proposal deals on certain terms that will be govern the relationship between one parties enter into the legal binding agreement with another parties. The offer can be made orally, written documents or implied by conduct. An invitation of treat is not an offer but an invitation to other persons to make an offer and cannot create an agreement if there is a purported acceptance. The main difference between an offer and an invitation to treat is that a person making an offer intends to be bound, whereas a person making an invitation to treat does not intend to be bound.
An advertisement of reward in newspaper is only an invitation of treat the public who make offer the contract about the reward the second party may accept or reject the offer.
Fitch v Snedeker 38 NY 248 (1868), Snedeker offered a reward to anyone who found and return the dog. Fitch found the dog and returns it to before being aware of the offer made by snedaker. The court was held that Fitch would not be entitled to reward. This is because acceptance of an offer, in ignorance of offer, is no acceptance and does not confer any on Fitch. A person who gives information without knowledge of the offer of reward cannot claim the reward. 
Another famous case R v Clark (1927) 40 CLR 227, a reward was offered for information about murder of two policemen. Clark was turned information relation to murder case to police about those who committed to crime in order to save himself. The court held that Clark was not entitled to reward for the information he provided the police in order to a protect himself of a wrong charge of murder case. In order for a person to have accept an offer, the acceptance must be in response to the offer, therefore there was no acceptance offer from the offeror and there were no contract between both parties. 
When the loss property involve, the some case that provided for a reward for the finder for preserving the property. But in this case the owner of dog give the advertisement in a lical newspaper for reward who return the bonzo as a perfect condition and health.
Apply relevant law to the fact and the problem question
According to the Fitch v Snedeker case reward is not offer only an invitation of treat. Similarly, applying the case R v Clark an advertised reward in newspaper or notice board is not legally made offer. It is only an inviting offer in the before made an offer. In these case Clark claim the reward to give information about the murder.
Applying both cases Jane who makes an offer to entitle to reward to return the bonzo the owner of bonzo can refuse or accept Jane offer. The owner of bonzo put some of the terms and condition when the advertisement clearly indicate that it is not an offer or the party who advertised may find themselves defending a contract law case in court. So acceptance must be made with knowledge of the offer.
In this case Jane is not entitled to reward money. There is no any contract between Jane and the owner of bonzo until the owner accepts Jane Offer. Also Jane did not apply the terms and condition of advertisement which is she has to return bonzo in a perfect condition. When she return the bonzo, His lags indicate that something wrong in the health.