$ mkdir x
$ cd x
$ echo aa > .y
$ mkdir y
$ echo aa > y/z
$ echo aa > y/.z
$ grep -r a *
y/.z:aa
y/z:aa
It's kind of a gotcha. Fortunately one rarely finds dotfiles in subdirs.
The reason there are files that start with a dot is that ls(1) and globs starting with an asterisk ignore them by default. ls needs -a (all) to show them. Some shells, but not bash, provide a globbing syntax for the recursive expansion you think you require here.
But if, as normal, you want to grep recursively down from the current directory then that's what you should specify; just pass grep one path to search, dot, the current directory.
grep -r foo .
grep will run through all those files, if any, and recurse through all the directories, if any. grep recursing down a directory will process all the files/subdirs in that directory. (which includes . files).
If the shell can't expand the * , grep will receive a literal * and try to open a file/directory named * .