Tendinitis is not a product of a bad grip or bad form, it's from gripping an object and increasing muscle tension...its created by the stretching of the tendons or overuse unnaturally...gripping a bowling ball (or a tennis racket) is not a natural motion...plain & simple

 
 
A stretched span with a lot of reverse can promote gripping and muscle tension. Additionally, the gripping can cause a tendency to want to slightly bend the elbow during the swing to stay under the ball. This certainly is what triggered my Medial epicondylitis (Golfers elbow) 10 years ago.

 

Once you've damaged tendons you can never repair them completely, an athlete merely want to not damage them any further...as noted proper stretching recommended by a sports doctor understanding the tendons that are damaged and the proper stretches to 'repair' and wearing a compression sleeve will help in keeping the tendons warm and supportive...

 
 
Actually, soft tissue therapies (ASTYM, Graston, ART) have advanced significantly over the past 20 years. They do wonders for regenerating tendons and removing scar tissue.
 
I went through several months of ASTYM and ART after giving up on all traditional (and some non-traditional) remedies. Rest, Ice, Compression, elevation (RICE) didn't cut it. Ultrasound at the Chiropractors office was a waste of time. Acupuncture just turned out to be painful torture.
 
Soft tissue therapy in conjunction with appropriate stretching did the trick. I went from barely being able to lift a cup of coffee to bowling again without limitation.

I'm not sure about the statement of "you can never repair them completely". If you can regain all the strength and flexibility you had before the injury, I think that's all that really matters.