I don't see how it's odd and I think it's unnecessary to add that. However I will leave this open for a bit to see what others think.

What Unix umask could come up with that combination?
Impossible. Thus very odd indeed!

I don't see any harm in documenting the mode (0750) it uses to create dirs with this option.

Also, there definitely needs to be a way offered for the user to change it. One might expect the user to simply use a different umask. However that would also change the modes of the files being downloaded, in addition to the directories being created.

Private directories and non private files, are just the same valid choice as non-private directories and private files. So the program should offer the user more flexibility.

there definitely needs to be a way offered for the user to change it

This option has existed in curl since December 2002 without that ability. I'm not sure saying it needs to be offered is correct; clearly people have managed without it.

You can easily change the mode after curl is completed if you want something different and changing the umask isn't enough. Is it really that important that curl does it by itself?

Well let's put things in perspective. It is curl that is changing
things, and the user needing to repair them back.

The user has set a umask, and curl has overridden it, and only in
certain cases (directories) too.

So the user needs to make odd scripts like

find -type -d -perm 0750 -cmin -10 -exec chmod <mode that would have been made with user's umask> {} \;

to "repair the damage."

Anyway, curl can go on making directories 0750, but the man page should
say what find(1) invocation would be best to "repair the damage" if the
user wanted to "repair the damage".

Also document the severity of the override: Does it combine 0750 with
the umask if more restrictive, creating e.g., 0700. Or does it create
0750 no matter what.

The user has set a umask, and curl has overridden it,

No it hasn't. The user's umask still masks off bits accordingly, as that's done by the mkdir function. Explained like this in my mkdir(2) man page:

The argument mode specifies the mode for the new directory. It is modified by the process's umask in the usual way: the mode of the created directory is (mode & ~umask & 0777).

... where mode is 0750 in this case.

I'd call it inform rather than warn, but sure - feel free to propose a text for the man page!

We can of course also consider changing the mode we use.

We didn't "inject" any "funny" umask. We use a mode. You can't use mkdir() without one.

I'm trying to work and be constructive here. It would be nice if your snark and attitude could be taken somewhere else.

OK, it seems it would be best to do as in tests/testcurl.pl:

mkdir $build, 0777;