You could maybe remove that quadrant strip profile, which they have put on to disguise it and have a special profile made up by a specialist to replace it.
If there is a wall on both sides of the stairs there will be a full stringer on both sides. If one side or the stairs is open and the stringers are like those in the picture below:-
Then you have a mixed construction, one side cut, the other full, sometimes called a half cut stringer stair. Most commonly, though, stairs in the UK have full stringer construction simply because it is a lot faster, easier and cheaper to make. It is also potentially somewhat stronger
Either way you shouldn't modify the full stringer by cutting material away because both the treads and risers are held in place by glue and wedges at the back. Any substantial amount of cutting away the stringer can weaken the stringer and/or displace the wedges. Just don't do it!
The way to deal with this is often to form a moulding during manufacturing on the top of the stringer which matches the skirting moulding. The extra thickness of the stringer over skirting (often 28 to 38mm vs. 18 to 25mm of skirtings) is sometimes hidden by installing the stairs prior to installing the MF studwork and its' plasterboard on top of the stringer, thus reducing the visible thickness. This sort of detail needs to be in the original design, though, and is difficult to achieve after the stairs are installed
If I may? Do you like that skirting?
It's an horrible detail, can you:
1/ not get them to snag it and point out the dodgy beading and the detail?
2/ change the skirting to something more appropriately sized, height wise?
So that it runs into the stair stringer.
3/ Take that manky beading of and cut the skirting at 45 degrees that top corner.
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