I googled "delayed ICSI" and I think it is the same thing as a "rescue ICSI". It is ICSI done the next day after finding none or very few eggs have fertilized naturally. Sound just like my scenario. Unfortunately, the research findings is not very positive. Success rates for rescue ICSI is pretty low.
Gosh, this is hard. I need to stay away for Dr. Google!
(**Updated: I found out during transfer that delayed ICSI meant the mature eggs were ICSI'd right away, and then they let the immature ones mature one more day before they were ICSI'd the next day.)