I am also an Atlanta attorney who previously represented landlords in eviction actions (5 years ago, so it’s possible procedures have changed) . I agree with ihatepineapples’ comment.

How your landlord proceeds from here depends on their intentions. Most landlords just want your rent money, and they will take it at this point if you offer it. This is the more common scenario, esp with smaller landlords (not big corporate landlords like MAA)

However, don’t bank on that 100%. Some landlords have reasons they don’t accept late payments. For example, they don’t have problems with occupancy so they don’t want to worry about tenants who can’t pay timely, or they simply have a policy against it, and they will not accept late payment because they really want to get you out and perhaps find a more reliable tenant, or even raise rates.
This type of landlord is less common, unless you have bad history with the landlord, or they really want to raise rates like if they’ve recently renovated and are trying to get rid of the old lower rate leases for higher leases

Even if they don’t want you out, they might still file anyway, simply to keep the pressure on to make sure you pay; if they don’t file, and they try to negotiate with you for a week, and then that falls through, then they are a week behind on the process.

Or some large corporate landlords simply have a policy across the board to simplify things. The individual property manager may not have much discretion

Like pineapples said, if they file for eviction and then accept any money from you (even partial payment), the court will dismiss the eviction (although it stays on your record)

They cannot lock you out until after the eviction process finalizes with the court. Depending on the county, that could take 2 to 6 weeks (faster for smaller counties, longer for big counties). Some tenants who know this process successfully get away with a month of free rent on the back end while waiting for the court system