battery damage
the converter will be drawing power, from th inverter aka batteries
trying to charge the batteries
its and endless loop loosing power
example my converter is 75 amps charge, my inverter is 2000w
if i forget to turn off the converter
the inverter draws 89 amps to power the converter, while the converter is charging at 65amps using the inverter for power
according to the numbers i saw on my meters
this is a 24 amp loss all in conversion use , mainly heat
each unit is only about 85% efficient, so each one looses/uses 15%
this does a number on my batteries real fast
you must find a way to turn off or unplug the converter
or go back to using extension cords
from the inverter to your TV etc..
your converter is probably NOT that large
but it is still an endless loss that is not needed and will eventually hasten battery death