Cheap modified sine wave inverters (and even expensive ones for that matter) can and do regularly damage/fry/ whatever expensive electronics. One of my employees plugged his Apple laptop into my 240w MSW inverter despite my warning not too. It cost him a new computer. I have a customer who destroyed the electronics in 2 brand new gas ranges at his off grid cabin before realizing it was the MSW inverter doing it. Just about everyone agrees that the control to an electric blanket will be smoked by a MSW inverter. I've run a TV form a MSW inverter and lots of diagonal lines appeared on the screen. Hum appears in the audio of electronics. Just about any Apple computer product will likely be damages. Clocks will not keep correct time. Lots of cordless tool battery chargers will be damaged by a MSW inverter.
I could go on. For charging expensive electronics the inverter you have is about the best you can get. Any little light weight cheap Radio Shack or truck stop special inverter can cause the type of damage I've listed above.
It's your choice.