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Bit late to the game with this but it's hard to tell from the picture if the white stuff is stuck on the plaster.
If the white stuff is some type of plater that's been used to stick something in place then use a very sharp blade to scrape it off as carefully as possible and use some toupret TX110 to fill any damage to the surface.
Scraper blades are great for this job but they need to be honed through use or by hand to work really well. There are cheap packets of scraper and filler blades available, often called euro style :-
The scraper ones normally have a different colour handle and are slightly stiffer.
You're right that a load of kit would make this job easier but you should be able to manage it with some simple ones. It's one of those jobs where you try a few different tools to see what works best.
How should I fix this? I’m not really up for buying a load of kit to plaster <1m2 but I do have tiling/grouting tools.
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