By using law of total expectation: $$\mathbb{E}[e^{tXY}] = \mathbb{E}[\mathbb{E}[e^{tXY}|Y] = \mathbb{E}[e^{tXY}|Y=0]P(Y=0) + \mathbb{E}[e^{tXY}|Y=1]P(Y=1) = \mathbb{E}[e^{0}]0.7 + \mathbb{E}[e^{tX}]0.3 = 0.7 + 0.3M_{X}(t)$$
Ismael
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