I have experience using Mypaint and have recently begun using Krita. When I try to erase using "E", it erases the background and I see the checkered squares. How can I erase only the pixels drawn ?

In applications like mypaint, photoshop or gimp, the background, that is default or first layer in these applications doesn’t have an alpha channel by default. so, on their background layer, the eraser does not erase, but paints in the background color.

In Krita, all layers have an alpha channel, so if you want to paint in the background color, you should do that, instead of erasing. You get the same effect in, say, gimp, if you create new image, add an alpha channel and then use the eraser tool. Most Krita users actually on starting a sketch in Krita add a new blank layer first thing they do (the INSert key is a useful shortcut here.) That doesn’t use extra memory, since a blank layer or a layer with a default color just takes one pixel worth of memory.

You can also set a default background color in image/properties.