Recently Taniguchi and Ohyama found that the higher (CO)-C-12 to (CO)-C-13 integrated intensity ratios at a transition J = 1-0, R = I((CO)-C-12)/I((CO)-C-13) greater than or similar to 20, in a sample of starburst merging galaxies such as Arp 220 are mainly attributed to the depression of (CO)-C-13 emission with respect to (CO)-C-12. Investigating the same sample of galaxies analyzed by Taniguchi and Ohyama, we find that there is a tight, almost linear correlation between the dust mass and (CO)-C-13 luminosity. This implies that dust grains are also depressed in the high-R starburst mergers, leading to the higher dust temperature (T-d) in them because of the relative increase in the radiation density. Nevertheless, the average dust mass (M-d) of the high-R starburst mergers is significantly higher than that of non-high-R galaxies. This is naturally understood because the galaxy mergers could accumulate a lot of dust grains from their progenitor galaxies together with the supply of dust grains formed newly in the star-forming regions. Since L (FIR) proportional to MdTd5 given the dust emissivity law S-v proportional to lambda(-1), the increases in both M-d and T-d explain well why the starburst mergers are so bright in the far-infrared. We discuss the important role that the superwind activity plays in destroying dust grains as well as dense gas clouds in the central region of mergers.