In a map view you see 2 actions to add a new row:

How to hide BOTH buttons
- Go to Data > Tables and open the table
- Under "Are updates allowed" use an expression to only disable adds in map views with an expression like
SWITCH(CONTEXT("ViewType"),
"Map", "UPDATES_AND_DELETES",
"ALL_CHANGES") - Or disable "Adds" if you never need to add new rows to the table.
How to hide the ADD button
- Go to Actions and open the system generated Add Action
- Set PROMINENCE to "Display inline" if you still need the Add Action in another view.
- Or to "Do not display" if you never need the Add Action.
- Or use an expression in "Only if this condition is true" to only disable adds in map views with an expression like
CONTEXT("ViewType")<>"Map"
How to hide the PIN button
- Add a virtual column to your table. Let's call it Address_VC
- Under "App formula" enter your address column like [Address]
- Go to the map view and change the "Map column" to [Address_VC]