Maybe, this problem is why the last owner got rid of the machine.
The first essential has to be getting the base to locate properly on the bedways.
If the Vee in the base is not sitting firmly on the Vee of the bed, the reason for that needs to be found. The bruise is a good starting point. There needs to be a slight clearance between the base and the bed, to allow for when the clamp is tightened.
It may have no effect, but the clamp is not symmetrical, so may contribute to sideways movement when tightened. Have not checked my mini to see if fitting the clamp "wrong way round" is either possible, or will produce lateral movement.
As already advised, remove any obvious damage marks and then use engineer's blue to check for a fit, without the clamp, and then when clamped..
Bear in mind that it is possible that the Tailstock body may be offset so far from the base that tightening the clamp, with an excess displacement may be a contributory factor to the movement.
As an aside, I was given a Tailstock with a lever lock, instead of the screw type clamp. It was WAY off centre (5mm ) on my machine. Stripping it showed that the abutments for the lateral grubscrews looked to have been "machined" with an angle grinder. Milling both faces flat, and taking more off one than the other allowed the Tailstock to be aligned, although one side then required a longer grubscrew.
As always, detailed examination will reveal the cause of the problem.
Howard