Getting over it means simply that it wouldn't be a constant cause of sorrow or a daily life disruptor for you. "Get over it" seems just harsh in this context as if trying to rush someone, but "you will get over it" depending on the wording, while seemingly obvious advice should remind you that as time goes on the bad feelings will affect you less and less.

This in no way should mean that you should actually forget that the person existed, but more like to be "okay" with it, and accept it.

You are not getting over the person like in a break up, you are getting over the fact that they died. The "it" refers to the event and being okay with it.