Firstly, congratulations on your acquisition. :thumbsup:
Not sure if your GL has an alarm but if it has the remote keyless system, I'd bet you dollars to donuts that it does.
There are actually three styles of remote for the SM body Santa Fe. Allow me to break it down for you:
2001-2002: 2-button remote (no Hyundai logo)
2003: 3-button remote; logos printed on and easily wear off - 'HYUNDAI' is stamped at the bottom
2004-2006: 3-button remote; logos stamped in and do not wear off - Hyundai logo is stamped at the bottom.
Luckily for you, the version with the stamped buttons is compatible with your 2003 and it's crappy printed icons. :w00t:
Here is one for sale on eBay.
Programming instructions are
here. Just FYI, the switch they are referring to is just above the OBD port under the driver's side crash pad.
Good luck.