  In this paper we show that an immersed nontrivial translating soliton for
mean curvature flow in $\mathbb{R}^{n+1}$($n=2,3)$ is a grim hyperplane if and
only if it is mean convex and has weighted total extrinsic curvature of at most
quadratic growth. For an embedded translating soliton $\Sigma$ with nonnegative
scalar curvature, we prove that if the mean curvature of $\Sigma$ does not
change signs on each end, then $\Sigma$ must have positive scalar curvature
unless it is either a hyperplane or a grim hyperplane.
