General Discussion

FWIW, Gemini's take on it. Note it even mentions hand shaking. Who knows, maybe it's multiple factors.

1. Senile Purpura (Actinic Purpura)

Medical experts note that the most probable culprit for recurrent bruising on the back of the hands in older adults is senile purpura.  
As people age, the skin and the connective tissues supporting the blood vessels thin out, and the blood vessels themselves become fragile.  

Combined with cumulative sun damage (common in avid golfers), even microscopic, unnoticed trauma can cause these fragile capillaries to rupture, leaking blood under the skin and creating prominent, long-lasting purple bruises.  

2. High-Dose Aspirin or Anticoagulants
The White House medical staff has publicly stated that Trump takes 325 mg of aspirin daily as part of a standard cardiovascular prevention regimen.  

Aspirin irreversibly inhibits platelet activation, meaning blood does not clot as quickly.  

At 325 mg (which is higher than a standard 81 mg "baby" aspirin), the risk of easy, pronounced bruising from minor bumps is significantly amplified.

3. Vigorous Handshaking
Both Trump and White House medical statements have explicitly attributed the bruising to "soft tissue irritation from frequent handshaking." For someone on daily blood thinners with thinning skin, shaking hands firmly with hundreds or thousands of people can cause enough minor, repetitive pressure to trigger localized bleeding on the hand.  

4. Minor Sports Trauma
As an avid golfer, grabbing tightly packed clubs out of a bag, minor mis-hits, or the repeated friction and pressure of gripping a golf club can easily cause superficial bruising when combined with the thinning skin and aspirin use mentioned above.  

5. Chronic Venous Insufficiency (CVI)
Official statements have also referenced Chronic Venous Insufficiency, a circulatory condition where vein valves (typically in the legs) weaken, causing blood pooling, swelling, and increased venous pressure. While CVI primarily causes swelling in the lower extremities, it reflects a broader fragility in the vascular system that contributes to easy bruising and skin discoloration.