Its entirely up to you

If you had written the adventure yourself this is something you may have decided when you wrote it, or it may be something you think about as the characters develop in playing, or a bit of both.

Personally, as there is no indication that Glassstaff has changed his appearance, there would be no reason that Sildar would not recognise him. Your role as DM is to play both NPCs reactions in accordance with your take on their personalities.

By the way, this is not something you can be wrong about.

Make the townsfolk afraid of them, too.

In short: have the NPCs react like real people.

It's a small town. People talk. People are going to notice the destroyed door, and others may have been drawn to the ruckus and seen/overheard what happened. Then the rumor mill got to spinning.

See, in this case...

The town has spent the past period of time being dominated by the Redbrands, living in fear of them.

So...in rolls this band of strangers, wipes out their old oppressors, then kicks down the door to their townmaster's home, terrifies him and his daughter, and (depending on what was said) may have just informed him that they are seizing control of the town.

Great.

So, by the perspective of the average townsperson, they've just traded one tyrannical group of thugs for another that's even stronger.

So, this could play out in a few ways...

• Townfolk avoid them like the plague, doors are locked, and everyone is extremely nervous in trading with them.
• Someone in town tries to get word out to call for help to get rid of these 'new tyrants.'
• Quest-givers are leery of them and hesitant to ask them for help (they certainly weren't asking the Redbrands for help with all these issues).
• They visit a shop and the shopkeeper flinchingly gives them money...the 'protection' he was supposed to be paying to the Redbrands, and assumes the PCs are there to demand. Make sure he tells them why he's giving it to them. Make sure he gets panicky (thinks his shop is now marked for destruction) if they refuse it.
• Guard-force/militia is cautiously hostile towards them--not willing to start a fight, but is not at all friendly.

Assuming the party notices what is going on, Sildar or anyone else who somewhat trusts them can give them an extremely short line, something like...

This town just spent who-knows-how-long being ruled by bandits...and your first act after killing the bandits is to break down the door of the townsmaster, threaten him in front of his daughter, and announce that you were seizing control of the town. What'd you think was going to happen?

No need for an extensive lecture

Fixing it

The PCs have made a really, really bad first impression on the town. It's going to take a bit of effort to convince them that they are, in fact, the good guys and not a rival group of thugs that just took over some territory from the Redbrands. Public apologies, repaying protection money, distributing loot from the hideout, etc. may help with this. As will time, with the PCs doing quests and such to help the town.

How it went when I did something like this

Not with LMoP, but I've done stuff like this in the past. When a PC party is too heavy-handed and forgets that NPCs are people, I tend to draw in reactions like this. The town ends up afraid of them, people start avoiding them, and generally treating them like a gang of unstable violent thugs. "Don't provoke them, but try to get them to go away" is the name of the game.

This usually gets the point across to my players without having to lecture them. It's a case of 'show, don't tell.' You show them the consequences of their actions instead of just telling them about it. I've had one group of players who ended up just rolling with it, and ruling a town as a band of little tyrants (and that complicated life for them in several ways throughout the adventure), but they liked their rulership enough that they didn't care. But, by and large...NPC reactions to PCs tend to be a good indicator to players of how their characters' actions are being perceived.