The oocyte doesn’t have a direct way of recognising that sperm is stressed. However, stress does weird things to cells (the sperm, in this case), and the conseq

The oocyte doesn’t have a direct way of recognising that sperm is stressed. However, stress does weird things to cells (the sperm, in this case), and the consequences of that are often severe. This definitely has an effect on the fitness of individual sperm cells, and purely stochastically this means that it’s more likely for healthy sperm to inseminate the egg. And after the fusion of sperm and egg, stressed sperm likely exhibits genetic damage (despite the topic on hand being non-genetic information), and this in turn makes it less likely that the zygote (fertilised egg) will be able to divide correctly. This leads to a spontaneous abortion of pregnancy — a process that naturally occurs more frequently than actually successful pregnancies (this happens within days of fertilisation and goes unnoticed). So to answer your question: the egg itself probably doesn’t have a way of sensing this directly but there are many factors that indirectly have a similar effect. Stressed sperm is selected against.