Which of the following metal carbonyl $\mathrm{C}-\mathrm{O}$ bond order is highest?

When compared to other metals, the Mn has a positive charge. As a result, giving up its electron density to the antibonding orbitals is difficult for manganese. Mn would thus create a weak metal–carbonyl connection.

As charge on C.A. $\downarrow ,C-\mathrm{O}$ bond strength $\uparrow$

 or $\mathrm{C}-\mathrm{O}$ bond order $\uparrow$ or $\mathrm{C}-\mathrm{O}$ bond length $\downarrow$

Hence correct option B.