The scalar spectral index (usually denoted '$n_s$') describes how density fluctuations vary with scale. An index of unity means that the variations are the same on all scales. $n_s$ is an input parameter to $\Lambda$CDM, and influences the characteristic size-scales of structure formation (where this small of an adjustment has little effect). Inflationary models, on the other hand, do generally suggest particular values (often ranges) of $n_s$, and $n_s = 0.96$ is still very compatible with current models of inflation.
The plots I've seen definitely state that $n_s$ effects the number of e-folds, but I'm no expert on the subject, and will refrain from conjecturing wildly. I'd recommend taking a look here, and the references there-in.