We report on the results of a joint experimental and numerical study on the sub-cycle laser field-driven electron dynamics that underlie the population of highly excited electronic states in multiply ionized argon dimers by electron recapture processes. Our experiments using few-cycle laser pulses with a known carrier-envelope phase (CEP) in combination with reaction microscopy reveal a distinct CEP-dependence of the electron emission and recapture process and, furthermore, a small but significant CEP-offset to the scenario in which no excited argon dimers are produced. With the help of classical ensemble trajectory simulations we trace down these different CEP-dependencies to subtle differences in the laser-driven sub-cycle electron trajectory dynamics that involve in both cases the transfer of an electron from one argon ion across the system boundary to the neighboring ion and its transient capture on this ion.