  It is known that any surface knot can be transformed to an unknotted surface
knot or a surface knot which has a diagram with no triple points by a finite
number of 1-handle additions. The minimum number of such 1-handles is called
the unknotting number or the triple point cancelling number, respectively. In
this paper, we give upper bounds and lower bounds of unknotting numbers and
triple point cancelling numbers of torus-covering knots, which are surface
knots in the form of coverings over the standard torus $T$. Upper bounds are
given by using $m$-charts on $T$ presenting torus-covering knots, and lower
bounds are given by using quandle colorings and quandle cocycle invariants.
