The answers provided by Niel B and CaM are good (and both have my upvotes), but I want to emphasise another aspect of this, based on my own experience with running this adventure (although this exact thing didn't happen to me; the first long rest was some time after this):
Level 1 characters are weak as hell, and this first dungeon is quite difficult for level 1 characters.
I agree that their carelessness should have an impact on the goblins, but I would advise away from anything too gameplay related like extra traps or extra enemies. Instead, I would focus on the roleplay and environment.
Stealing from Niel B's answer:
The bodies are gone. The entrance has been re-covered. Goblin sentries are hiding in the bushes. Have the goblins call them by name to signify they've been spied on.
The bodies being gone and there being goblins in the bushes (assuming these are from another area, not extra goblins) who address them by name are nice touches expressed through narrative to show the players that their actions have in-game consequences.
Also stealing from CaM's answer:
... once the goblins were alerted to the PC's presence, drums began beating. That helped keep the goblins from forgetting that they were at "red alert" status. Hearing those drums would warn your PCs that things were not on a peaceful footing. This might be enough for the wiser of the PCs to want to enter with more caution than usual. Maybe.
This, again, shows a narrative feature (the sound of drums that wasn't there before) that shows that your party's action have consequences, and although goblins will now be paying more attention, if there's still the same number of them in the same rooms, not much has changed regarding the dungeon's difficulty, but the goblin's behaviour has, which may give the party a harder time sneaking up on them or something, but otherwise doesn't make the dungeon any harder.
As for traps, I dismissed them just now, but it might be good if you add a couple of obvious traps, or something that your most perceptive PC would be able to spot with their passive perception (so the traps don't have to be super obvious, but will still be spotted by at least one of the party); this way, it won't make the dungeon any harder than it already is (you don't actually want to punish your players, simply teach them that the world reacts to them), but it shows some effort on the goblin's part to counteract their actions, just not successfully enough to actually change the difficulty of the dungeon.
I wouldn't recommend pulling punches quite as much as this ordinarily, but they're level 1! Level 1 characters are weak as hell, like I said. Saying that, level 3, for example, they won't be as weak, and if they haven't learned yet, then not pulling punches might teach them to start paying attention. But this early on, they're still learning, and they're still weak, so try to show the consequences in a narrative way, rather than a gameplay "punishment" way.