Grep could have been called "filter" in array context.
Most common form is @output = grep{anon_sub_returning_True_False}@input;
This code:

#!/usr/bin/perl -w
use strict;

my @a = qw( a b c d ); 
my $i=0;
my @b = grep { push(@a,'!') if !$i++; 1 } @a; 
print "@b\n";
print "@a\n";
__END__
output:
a b c d
a b c d !
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Means take each item in @a and put it into the anon grep subroutine. If that subroutine returns true, then move that item to @b. Absent an explicit return statement, the return value of a Perl sub is the last statement. In this case it is "1", or always true. So this is the same as: @a=@b; as far as grep{} is concerned. This push statement gets executed but has no bearing upon the action of grep{}.

So, YES grep{} is meant to process/filter lists! I would argue that putting this push statement inside the grep is a weird thing to do.

grep does have a scalar context also! This is useful in some cases, here this is just a "dumb" example.

my $num = grep{1}@a;
print $num; ##prints 5 (num of elements in @a) ie, abcd!
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But this can be used to say count number of matches in @a.
$num = grep {/some_regex/}@a;
But of course most common use would be @a=grep{/regex/}@b; which moves any item from @b which matches regex to @a.

Update:Perl will not allow the input list to be modified within the grep{} subroutine. This could create a circular endless loop and that just won't happen.