By RAW, a goliath is acclimated to high elevations. Even if your players never go up a mountain, the goliath is still acclimated.
By RAW, some backgrounds give perks, such as saying that the PC can expect some accommodations with certain groups of people. If you, the GM, arbitrarily decide to ignore the RAW because you don't want it to work that way, then the decent thing to do would be to tell the player ahead of time you're ignoring the RAW.
It would be like if the player's backstory said their goliath was born on the plains instead of the mountains, so you decided that means they don't have resistance to cold damage--but you didn't bother to tell the player that until they actually got hit by an attack that did cold damage (or give them a different damage resistance in place of cold).
So do you need to tell them? No. But you should, unless you want to be a jerk about it.
"Hey, so you've made a criminal. But we're playing Curse of Strahd, where you get sucked to another plane of existence. You're not going to have any criminal contacts. Do you care about that, or do you want to figure out a new background feature to replace that?"