Hi Julia,
Did you meet with a board certified lactation consultant? If your baby is properly latched it is impossible to "clench". You can find a board certified lactation consultant here:
www.ilca.org Just click on the "Find a Lactation Consultant" button at the top of the page.
If your baby is gagging, the tube is in too far. She should not sense it. It is placed after the latch, in the corner of baby's mouth, only about 3/4 inch, enough for the suction to withdraw the fluid. Once you get the hang of it, it makes life a whole lot easier and the action of baby at the breast will help to build your milk supply.
Also, if your baby is already back to discharge wt, she's in good shape. We like to see a trend toward back to birthweight by 3 weeks of age.
Keep up the great work!
Best, Lenore