  Because of strong and spatially highly variable interstellar extinction and
extreme source crowding, the faint (K>15) stellar population in the Milky Way's
nuclear cluster is still poorly studied. RR Lyrae stars provide us with a tool
to estimate the mass of the oldest, relative dim stellar population. Recently,
we analyzed HST/WFC3/IR observations of the central 2.3'x2.3' of the Milky Way
and found 21 variable stars with periods between 0.2 and 1d. Here, we present a
further comprehensive analysis of these stars. The period-luminosity
relationship of RR Lyrae is used to derive their extinctions and distances.
Using multiple approaches, we classify our sample as four RRc, four RRab and
three candidates, ten binaries. Especially, the four RRabs show sawtooth light
curves and fall exactly onto the Oosterhoff I division in the Bailey diagram.
Compared to the RRabs reported by Minniti et al, 2016, our new RRabs have
higher extinction (A_K>1.8) and should be closer to the Galactic Centre. The
extinction and distance of one RRab match those for the nuclear star cluster
given in previous works. We perform simulations and find that after correcting
for incompleteness, there could be no more than 40 RRabs within the nuclear
star cluster and in our field-of-view. Through comparing with the known
globular clusters of the Milky Way, we estimate that if there exists an old,
metal-poor (-1.5<[Fe/H]<-1) stellar population in the Milky Way nuclear star
cluster on a scale of 5x5pc, then it contributes at most 4.7x10^5 solar mass,
i.e., ~18% of the stellar mass.
