So - If I control a dude with puppet that has 4 bounty and a control point from Desolation Row - does he lose his control point?
Yes.
And he will get it back again when puppet expires.
Des Row specifically states “your dudes with”. As that dude will cease to belong to the Des Row player, he loses any benefit for being “his/her” dude.
Unless of course you’re running some sort of Des Row hux deck yourself, in which case your Des Row will give him a CP. So while he would lose 1 and gain 1, the net result would effectively be no change.
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