There is tons of info online about this subject. I personally tend to disagree with some of it but there are things to be aware of when charging a bank of batteries that are either a different age, different type or different size. The battery life expectancy and the quality of the battery can be compromised if they are in a circuit with different batteries. Generally it is best to put 4 batteries in of the same age, size and type. If you do choose to mix batteries, keeping alike batteries together is important. If for example you had four 6 volt batteries for a 12 volt circuit and two were new and two were used with the same usage, it would be best to place the two new ones in series and the two old ones in series then place the old and new in a parallel 12 volt circuit. The problem is that the charging and discharging won't be in sync between all of the batteries which creates different charge cycles and profiles. The inverter charger won't know what state each battery is and nor does it care. It assumes that the voltage it reads is the voltage of all the batteries which is a good guess if all the batteries are the same age, type and size. It gets a little tricky especially if there are large differences in battery conditions. I will admit that I have mixed batteries but I also have carefully watched them. I did find a battery overcharged slightly at one point but it wasn't of great concern.
I currently have two house batteries alike and a older deep cycle battery I use for starting. All three batteries are charged off the engine alternator and I have not noticed any issue with that. I also combine the starter battery with the house batteries when idle for extended periods and plugged in to charge the starting battery. I have not had any issues at all. All three batteries are doing well and have good capacity.
My suggestion is too keep the batteries alike but on the other hand, if you have good batteries sitting around and the room to install them, use them but be aware of possible complications.