  It has been recently proposed that Hawking evaporation might slow down after
a black hole has lost about half of its mass. Such an effect, called "memory
burden", is parameterized as a suppression in the mass loss rate by negative
powers $n$ of the black hole entropy and could considerably extend the lifetime
of a black hole. We study the impact of memory burden on the Primordial Black
Hole (PBH) reheating scenario. Modified PBH evaporation leads to a
significantly longer PBH dominated stage. Requiring that PBHs evaporate prior
enough to Big Bang Nucleosynthesis shrinks the allowed PBH mass range. Indeed,
we find that for $n>2.5$ the PBH reheating scenario is not viable. The
frequency of the Gravitational Waves (GWs) induced by PBH number density
fluctuations is bound to be larger than about a Hz, while the amplitude of the
GW spectrum is enhanced due to the longer PBH dominated phase. Interestingly,
we show that, in some models, the slope of the induced GW spectrum might be
sensitive to the modifications to Hawking evaporation, proving it may be
possible to test the "memory burden" effect via induced GWs. Lastly, we argue
that our results could also apply to general modifications of Hawking
evaporation.
