Can walking in sun after 11 days damage implanted grafts?

Strong sun exposure does not really kill the follicles underneath the skin. But 11 days after surgery, your scalp still be fragile to sun burn. Please put on the cap or umbrella to protect your sensitive skin in the early period after surgery.

Walking in the sun most likely did not damage your grafts. But it would still be best to address your concerns with your doctor.  While short amounts of time would not necessarily be a concern in most cases, excessive and ongoing sun exposure can exert a detrimental effect on the follicles. This is supported by studies on identical twins who are genetically predisposed to pattern baldness. A twin who lives a lifestyle highly exposed to UV rays will display a much greater extent of hair loss. The sun’s energy can either affect the surface of the scalp directly, or by traveling through the hair shafts to the follicles themselves. Researchers believe that oxidative damage due to heavy UV exposure facilitates the aging processes of the follicles and contributes to hair loss. 
Following a hair transplant, brief and moderate sun exposure should not cause harm to the grafts. However, it would be wise to wear a head covering, especially as the skin is still healing.

It is best to contact your surgeon for post surgery issues and care since all doctors have slightly different instructions.