1. **State the problem:** Evaluate the expression $-2^2 + \left(-\frac{1}{3}\right)^{-3}$.\n\n2. **Recall order of operations and exponent rules:** Exponents are evaluated before negation. Also, for negative exponents, $a^{-n} = \frac{1}{a^n}$.\n\n3. **Evaluate $-2^2$ carefully:**\n$$-2^2 = -(2^2) = -4$$\nThe exponent applies only to 2, then the negative sign is applied.\n\n4. **Evaluate $\left(-\frac{1}{3}\right)^{-3}$:**\n$$\left(-\frac{1}{3}\right)^{-3} = \frac{1}{\left(-\frac{1}{3}\right)^3}$$\nCalculate the cube:\n$$\left(-\frac{1}{3}\right)^3 = -\frac{1}{27}$$\nSo,\n$$\frac{1}{-\frac{1}{27}} = -27$$\n\n5. **Combine the results:**\n$$-4 + (-27) = -4 - 27 = -31$$\n\n**Final answer:** $-31$