der Drücker
door handle
The handle on a door that you press down to open the door; a door latch or handle.
Der Drücker klemmt, ich bekomme die Tür nicht auf.
The door handle is stuck; I can't get the door open.

door handle / button / pushy salesman
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door handle
The handle on a door that you press down to open the door; a door latch or handle.
Der Drücker klemmt, ich bekomme die Tür nicht auf.
The door handle is stuck; I can't get the door open.

'Der Drücker' is derived from the verb 'drücken' (to press). The ending '-er' here refers either to a tool used for pressing (door handle, button) or to a person who does something (here: pressures someone).
Ich habe den falschen Drücker an der Fernbedienung erwischt.
I hit the wrong button on the remote control.
The context makes clear which meaning is intended. On a door, it is the handle; on a device, it is the button; and when it refers to a person who wants to sell something, it means the pushy salesman.
Der Drücker an der Haustür ist kaputt.
The door handle on the front door is broken.
In connection with a door, the most common action is 'den Drücker herunterdrücken' (to press down the door handle).
Man muss den Drücker fest herunterdrücken, um die alte Tür zu öffnen.
You have to press the door handle down firmly to open the old door.
In the meaning 'aufdringlicher Verkäufer' (pushy salesman), the word is colloquial and has a clearly negative, derogatory meaning.
Meine Oma hat sich von einem Drücker ein teures Zeitungsabonnement andrehen lassen.
My grandma was talked into buying an expensive newspaper subscription by a pushy salesman.
representative / substitute
'Vertreter' and 'Drücker' can both mean a person who wants to sell something. 'Vertreter' is neutral and can also sound reputable, for example at a company or in sales. 'Drücker' is colloquial and derogatory. It means someone who pushily tries to get people to sign a contract or subscription, often at the front door or on the street. The words can be confused because both have to do with selling. If you want to speak neutrally, use 'Vertreter'. If you want to criticize the pushy behavior, 'Drücker' fits.

Am Abend stand ein Drücker vor der Tür und wollte mir ein Abo verkaufen.
In the evening, a pushy salesman was standing at the door and wanted to sell me a subscription.
Nach dem Gespräch bestellt der Chef dem Vertreter einen Kaffee.
After the conversation, the boss orders the representative a coffee.