This article focuses on the characterization of a series of telechelic polybutadienes with acid end groups (PBd-COOH) neutralized with different alkali metal ions by elongational rheometry. Depending on the ion, the material is found to be strain-hardening or not. While the Li+ ions cause a strain hardening similar to that observed for low density polyethylene. Na+ and K+ essentially do not lead to any strain hardening. Rb+ leads to a different type of strain hardening, like sparsely branched polymers. It is also found that the material behaves brittlely at strain rates epsilon higher than the crossover frequency omega(c). Additionally, an esterified version of the material and the rubidium hydroxide neutralized PBd-COOH is characterized by Brillouin light scattering to assess the local chain dynamics, being essentially noninfluenced by the ion clusters. The dependence of the longitudinal sound velocity c(i) and hence the longitudinal modulus M from the phonon wave vector q and from the temperature T is compared for two different samples (with and without counterion). It is found that M is insensitive to the presence of the ionic clusters, and therefore, the local chain dynamics are essentially the same for the two model systems and do not play a role in the strain-hardening.