A semiconductor device has a semiconductor die with a plurality of bumps formed on contact pads disposed over its active surface. An encapsulant is formed over the semiconductor die. An interconnect structure is formed over the semiconductor die and encapsulant. The semiconductor die is mounted to a translucent tape with the bumps embedded in the translucent tape. The translucent tape has layers of polyolefin, acrylic, and polyethylene terephthalate. A back surface of the semiconductor die undergoes backgrinding to reduce die thickness. The tape undergoes UV curing. A laminate layer is formed over the back surface of the semiconductor die. The laminate layer undergoes oven curing. The laminate layer is laser-marked while the tape remains applied to the bumps. The tape is removed after laser-marking the laminate layer. Alternately, the tape can be removed prior to laser-marking. The tape reduces die warpage during laser-marking.