Sure that can be done, just remove those extra matching groups from your regex. Try following code:
$regex = '#(https?://[a-z0-9.?=+_-]*)#i';
$text = preg_split($regex, $note, -1, PREG_SPLIT_DELIM_CAPTURE);
Now resulting array will have 3 elements in the array instead of 4.
Besides removing extra grouping I have also simplified your regex also since most of the special characters don't need to be escaped inside character class.