  As a complementary study to that performed on the transverse momentum
($p_{\rm T}$) spectra of charged pions, kaons and protons in proton-proton (pp)
collisions at LHC energies 0.9, 2.76 and 7 TeV, we present a scaling behaviour
in the $p_{\rm T}$ spectra of strange particles ($K_{S}^{0}$, $\rm \Lambda$,
$\rm \Xi$ and $\phi$) at these three energies. This scaling behaviour is
exhibited when the spectra are expressed in a suitable scaling variable
$z=p_{\rm T}/K$, where the scaling parameter $K$ is determined by the quality
factor method and increases with the center of mass energy ($\sqrt{s}$). The
rates at which $K$ increases with $\mathrm{ln}\sqrt{s}$ for these strange
particles are found to be identical within errors. In the framework of the
colour string percolation model, we argue that these strange particles are
produced through the decay of clusters that are formed by the colour strings
overlapping. We observe that the strange mesons and baryons are produced from
clusters with different size distributions, while the strange mesons (baryons)
$K_{S}^{0}$ and $\phi$ ($\rm \Lambda$ and $\rm \Xi$) originate from clusters
with the same size distributions. The cluster's size distributions for strange
mesons are more dispersed than those for strange baryons. The scaling behaviour
of the $p_{\rm T}$ spectra for these strange particles can be explained by the
colour string percolation model in a quantitative way.
