Make sure you know what it really is. This may help you identify it. There's a chart on the side that shows most of the common types. Three prong dryer outlet is most likely a 10-30.Helpful post, my situation is different. I have electric dryer outlet in my garage with two 120s and a neutral (assumed), I want to replace that outlet with 14-50 for my M3. Can I hook up that third wire to ground in the new outlet? I am not sure if it is grounded or not at the panel but according to these posts all homes prior to 1996 (mine built 1993) were grounding the neutral.
NEMA connector - Wikipedia
First question: since it's in your garage, so probably close enough, why not just order the 10-30 plug adapter from Tesla and use your real Tesla charging cord with it? That is easiest, most obviously correct, most foolproof, etc than trying to change your wiring. But I'm already concerned by your mentioning of a 20A breaker. That wouldn't be right for a 10-30 outlet (that second number says how many amps it's supposed to be for), so I would worry a lot about just plugging in and using it as-is. You probably should have that looked at before using it.
Other than that, there may be possibilities of changing the outlet to something else, depending on what the wire size is or other things, but that's more detailed than I would want to recommend or explain for this kind of situation over the internet. Have an electrician look at it, and see what you can come up with.