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This all depends upon the pattern of these random tiles.  But if they are
composed of similar cells, you might have a large background of these
cells which are covered by blackout pieces.  The selection of the random
tiles would actually result in the capture of these blackout pieces.  This
way there will only be a single piece located in this area when you place
the playing pieces on the now exposed field.

Another way is to have the edges of the cells of these random tiles 
rendered seperately, leaving the center of the cell blank.  A square cell 
would need to have each of its four sides rendered. For cells of other 
shapes(triangles or hexagons) the angled sides would need to be render in 
sections.  For example, if the sides were two pixels wide they might need 
to be rendered in 4x4 pixel sections.  This would mean a lot of positions 
declared on the board in the implementation, but those positions which are 
used by the playing pieces need be the only ones which have links.