You do not need strengthening exercise because trigger finger is not caused by lack of strength in your finger, but it is an issue related to the tendon surrounding the joint. Exercises for trigger finger require a tender touch because you are not working on a healthy joint. Simply putting your finger in warm water and rotating it lightly is enough to warm up the tendons. You can also massage your finger to help regain its range of motion. Moreover, it is equally important to avoid repetitive gripping of objects until the issue has been resolved. Here are some specific trigger finger exercises that may help improve your condition.
Trigger finger (also called stenosing tenosynovitis) occurs when inflammation builds up within a tendon of a finger and causes it to involuntarily flex.  If the condition is severe, the finger gets stuck in a bent position and sometimes makes a snapping sound when forcibly straightened -- sort of like cocking the trigger of a gun, which explains the name. People whose job requires repetitive gripping are at higher risk of developing trigger finger, as are those with arthritis or diabetes. The treatment varies depending on severity and cause, which is why an accurate diagnosis is important.
As you’ve just heard in the video, trigger thumb is a common and debilitating condition. The tendons in your thumb and fingers are covered in a tunnel like structure of tissues that are called sheaths. If you have trigger thumb, your tendons have become inflamed. Because of this inflammation or swelling, your tendons are no longer properly gliding through your sheaths. When this happens, the base of your fingers may lock up, click, or pop. Essentially, your fingers get stuck in a non relaxed position. This has the potential to be a very painful and frustrating condition, as you lose the full function of your thumbs. This condition can happen to all of your fingers including your thumbs, index, middle, ring, and pinky.