Biological polymers hybridized with single-walled carbon nanotubes (SWCNTs) have elicited much interest recently for applications in SWCNT-based sorting as well as biomedical imaging, sensing, and drug delivery. Recently, de novo designed peptides forming a coiled-coil structure have been engineered to selectively disperse SWCNT of a certain diameter. Here we report on a study of the binding strength and structural stability of the hybrid between such a "HexCoil-Ala" peptide and the (6,5)-SWCNT. Using the competitive binding of a surfactant, we find that affinity strength of the peptide ranks in comparison to that of two single-stranded DNA sequences as (GT)₃₀-DNA > HexCoil-Ala > (TAT)₄T-DNA. Further, using replica exchange molecular dynamics (REMD), we show that the hexamer peptide complex has both similarities with and differences from the original design. While one of two distinct helix-helix interfaces of the original model was largely retained, a second interface showed much greater variability. These conformational differences allowed an aromatic tyrosine residue designed to lie along the solvent-exposed surface of the protein instead to penetrate between the two helices and directly contact the SWCNT. These insights will inform future designs of SWCNT-interacting peptides.