Drops of dried blood on the rubber glove dispenser at the phlebotomist's office. can i catch something since they drew my blood at that station?

Theoretical risk: Hepatitis transmission is possible. Wouldn’t worry about anything else. Make sure you are vacinnated against hepatitis B and ask your doctor about hepatitis C testing. I’ve gotten hepatitis C blood in my eyes and luckily not infected. Hopefully that can reassure you for now. I wouldn’t return to that phlebotomy site.

No: It is not a significant risk but the phlebotomist is required to change gloves before each patient.

Highly Unlikely: Unless you consumed the dried blood on the glove dispenser, which would be very unadvisable, you should not have had any exposure to blood-borne pathogens. Hope this helps!