The simple answer is nothing. Once the tenant has paid the rent according to the contract, you a) should not have a problem since they paid rent and b) also have a tenant who has complied with your notice.
By the time a three-day notice to quit or pay rent has been served upon the tenant, most landlords already want them out. The three-day notice becomes a pretext for getting rid of the troublesome tenant, although a perfectly legal one.
One of the question that often arises is whether the tenant can get a few days over the weekend past the three days. The answer is NO. Three days is three day from midnight of the day you served the notice.
Therefore if you served the notice on Thursday, count Friday, Saturday, and Sunday. Monday you can filed your complaint for unlawful detainer.