Why would the windows implementation of grep command here, from cmd, give an error message of trailing backslash?

Question

Why would the windows implementation of grep command here, and from cmd, give an error message of trailing backslash?

C:\Users\User>where grep
c:\cygwin\bin\grep.exe

C:\Users\User>c:\cygwin\bin\grep.exe --version
grep (GNU grep) 3.7
Packaged by Cygwin (3.7-2)
Copyright (C) 2021 Free Software Foundation, Inc.
License GPLv3+: GNU GPL version 3 or later <https://gnu.org/licenses/gpl.html>.
This is free software: you are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.

Written by Mike Haertel and others; see
<https://git.sv.gnu.org/cgit/grep.git/tree/AUTHORS>.

C:\Users\User>

I see and know that this works

C:\>echo a^"b | grep ^"
a"b

C:\>

now looking at linux

user@comp:~# echo ab\"c
ab"c
user@comp:~# echo ab\"c| grep \"
ab"c
user@comp:~# echo ab\"c| grep \"    <-- same command as above but with a space after the quote.
ab"c
user@comp:~#

Nothing strange so far.

Now looking at Windows though

C:\>echo a | grep \^"
grep: Trailing backslash

C:\>echo a | grep \^" <-- same command as above, but with a space after the quote.
a

This works

C:\>echo a^"b | grep ^"
a"b

C:\>

This gives an error about trailing backslash

C:\>echo a^"b| grep \^"
grep: Trailing backslash

C:\>

I don't understand why I get that error.

And this is related to that and also strange and I don't see why it's happening

If I put a space after that quote at the end then it doesn't give an error.

C:\>echo a^"b| grep \^"

C:\>

The above is looking for a quote followed by a space.

So if I do

C:\>echo a^"b | grep \^"  <--  a space after that quote. And notive also a space before the pipe
a"b

That works no error.

So for some reason, I don't understand why. The windows implementation of grep, gives an error about trailing backslash, when looking for just a quote.

I can't see how to produce an equivalent "trailing backslash" error with grep on linux.

I can get an error about a trailing backslash on linux, but not with a quote at the end.

# echo a\\b | grep \\
grep: Trailing backslash
#

# echo a\\b | grep "\\"
grep: Trailing backslash

I can see that to find a single backslash in linux, I need four. 'cos the shell goes for the four turns them to two. Then grep takes the two and turns it to one literal backslash.

# echo a\\b | grep \\\\
a\b
# echo a\\b | grep "\\\\"
a\b
#

And the trailing backslash in linux, means there's a backslash on the end that has special meaning, because it's not escaped, and it's not doing anything.

# echo a\\b | grep \\
grep: Trailing backslash
#

As soon as I stick a literal quote on the end, no error

# echo a\\b | grep \\\"
#
#

So why, when I give the windows implementation of grep, something that doesn't end in a backslah, it'd give the error about a trailing backslash?

Note that if I run this from cygwin, I don't get any error about trailing backslash

$ echo a\"b | grep \"
a"b

From cygwin it behaves a lot like the linux one

so gives that trailing backslash message under the same circumstances as the linux one

$ echo a\\b | grep \\
grep: Trailing backslash

and escapes backslashes fine and has no problem with the literal quote at the end.

$ echo a\\b | grep \\\\
a\b

$

$ echo a\\b | grep \\\\\"

$

Also, i'm on Win7, so no WSL feature