Because gravity on is about one-third of that on Earth, could you infer that Mars has more mass than Earth?

No, we can't infer from the lower value of due to gravity of Mars that it has more mass than Earth.

The force of gravity is explained . Taking extract from the linked answer.

The expression for the force of attraction between Mars and an object of mass ##m## is given by

##F_"mars"=GM_"mars"/R_"mars"^2m##, where ##G## is the Gravitational constant ##=6.67408 xx 10^-11 m^3 kg^-1 s^-2## Comparing with ##F=mxxa##, we obtain acceleration due to gravity ##g_"mars"## as ##g_"mars"=GM_"mars"/R_"mars"^2## If ##g_"mars"## is about ##1/3## of that on earth, from the expression we infer that this could be due to 1. Mass of Mars could be less than that of earth 2. Radius of Mars could be more than the radius of earth.

We know that equatorial radius of Mars is 3,397 kilometers as compared to 6,378 kilometers of earth. Calculated value of ##g_"mars"## from the above equation will be much higher than the value of ##g## of earth. However, ##M_"mars"## is ##6.42 xx 10^23kg##, about ##1//10th## that of Earth. The combined effect of smaller mass and smaller radius gives the lower value of gravity on Mars.