the 1990 650 engine is a piston-ported engine, not a case-reed engine, so it doesn't have any reeds. A little spit-back is normal for all piston-ported engines. The slide stop screws that RJ is talking about are on the side of the carb, it's the bigger screw with the exposed spring. The slide stop screw lifts the slide so you can set the idle. The air screw is the smaller one with the spring you can't see. The air screw controls the airflow to the pilot jet, which controls the air/fuel mix at idle.
If your shop says it's a bad reed, I would find a better shop, unless they were just throwing out ideas for you to look into...
Here's a link to a parts diagram for your sled
Alpha Sports - Arctic Cat Snowmobile Catalog
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2007 RMK 700 155", 2008 RMK 600 155", 2006 RMK 600 144", 98 Indy 440, 95 Prowler 550 2-up, 1990 Indy 650
RIP, destroyed by fire 1-22-2008

04 RMK 800, 05 RMK 600, 02 RMK 800, 97 RMK 700
http://www.avalanche.org/accidents.php