Odd entanglement entropy in T T<overline> deformed CFT2s and holography

We construct a replica technique to perturbatively compute the odd entanglement entropy (OEE) for bipartite mixed states in TT over bar deformed CFT2s. This framework is then utilized to obtain the leading-order correction to the OEE for two disjoint intervals, two adjacent intervals, anda single interval in TT over bar deformed thermal CFT2s in the large central charge limit. The field theory results are subsequently reproduced in the high-temperature limit from holographic computations for the entanglement wedge cross sections in the dual bulk finite cutoff Banados-Teitelboim-Zanelli geometries. We further show that for finite size TT over bar deformed CFT2s at zero temperature the corrections to the OEE are vanishing to the leading order from both field theory and bulk holographic computations.