Congratulations on your transplant.
Transplanted hair are usually shed between 4-6 weeks during a process called anagen effluvium. These hairs usually grow back after 3 months. By this timeline you should be in growth phase of transplant. Growing hair can not come out due to application of oil or gentle massage
What you are experiencing is perhaps minoxidil
induced shedding or shock
loss induced by hair transplantation
. The lost hair usually grow back.
Hope you find this answer useful. Feel free to ask further.