It depends. In general you cannot reconstruct the history how the one available matrix was generated from the matrix alone. You can just decompose the matrix into an equivalent translational and scaling transform (letting rotation aside as mentioned in the OP), replacing the transform of interest with its desired substitute, and re-compose, so that the translational part is not effected. But if the composition was done so that the position was effected by a scaling (as e.g. in S1 * T * S2), then you cannot eliminate scaling totally (AFAIK).
So in your case decomposition is relatively easy, because in a homogeneous 3x3 matrix without rotation there is an embedded 2x2 matrix that is effected by scaling only but not by translation. You get this sub-matrix if you strip the row and the column where in the 3x3 matrix the homogenous "1" is located. The resulting sub-matrix must be a diagonal matrix, e.g. only the values at  and  differ from zero. Those both values are in fact the scaling factors along x and y axis directions, resp. Hence setting both these values to 1 will do the trick.