The value of $$\left[5\frac{4}{9} \div \left(\frac{11}{4} - \frac{13}{6}\right)^2\right] \div \left[7\frac{3}{11} of 8\frac{4}{5} \div 1\frac{5}{7} - \frac{4}{3}\right]^2$$ is:

$$\left[5\frac{4}{9}\div\left(\frac{11}{4}-\frac{13}{6}\right)^2\right]\div\left[7\frac{3}{11}of8\frac{4}{5}\div1\frac{5}{7}-\frac{4}{3}\right]^2$$

$$=\left[\frac{49}{9}\div\left(\frac{33-26}{12}\right)^2\right]\div\left[\frac{80}{11}of\frac{44}{5}\div\frac{12}{7}-\frac{4}{3}\right]^2$$

$$=\left[\frac{49}{9}\div\frac{49}{144}\right]\div\left[64\div\frac{12}{7}-\frac{4}{3}\right]^2$$

$$=\left[\frac{49}{9}\times\frac{144}{49}\right]\div\left[64\times\frac{7}{12}-\frac{4}{3}\right]^2$$

$$=\frac{144}{9}\div\left[\frac{112}{3}-\frac{4}{3}\right]^2$$

$$=\frac{144}{9}\div\left[36\right]^2$$

$$=\frac{144}{9}\times\frac{1}{36^2}$$

$$=\frac{1}{81}$$

Hence, the correct answer is Option D