I have a 5.6 kW solar array installed with a 5.12 kW battery. However, by mistake installer put in a 8kW inverter instead of a 5 kW inverter. I am not planning on adding more panels. The installer agreed to correct their mistake and replace it for the 5 kW inverter. Should I replace it or leave 8 kW inverter in place? Does oversized inverter produce less energy than a matching inverter or I shouldn’t worry about it?

There will be a small drop in performance, but not enough to worry about.

 

A 5.6 kW_p system, can occasionally, produce more power. All down to how the modules are tested.

 

If it was me I'd be asking to have a very close look at the inverter datasheets to check things like efficiency at lower power, and start up conditions.  Your array is going the spend most of its life producing power well below it's rated max, so if your inverter isn't efficient at those because it's oversized (or hasn't even started up!) you might be wasting a lot.