The metal (Fe) makes the back bonding to $\mathrm{CO}$. The metal to ligand bonding creates a synergic effect which strengthens the bond $\mathrm{CO}$ and the metal ( $\mathrm{Fe}$ ). Which results in the contraction of $\mathrm{CO}$ bond length (Synergic means working together towards a common end. This is a bond formed by a ligand to metal ion which has a $\sigma$-bond from ligand to metal ion and the back donation of electron density from the metal to the $\pi^*$ orbitals on the ligand. Thus enhancing the acceptor strength of the p-orbital. Hence up to a point the effect of $\sigma$-bond formation strengthens the $\pi$-bonding or vice-versa. Due to this synergic effect bond order decreases.