The simplified value of $$\frac{\left(3\frac{1}{5} + \frac{3}{5}\right) \div \frac{8}{5}}{1\frac{1}{7} \div \left\{\frac{5}{7} + \left(\frac{1}{7} \div \frac{1}{3}\right)\right\}}$$ is:

$$\frac{\left(3\frac{1}{5} + \frac{3}{5}\right) \div \frac{8}{5}}{1\frac{1}{7} \div \left\{\frac{5}{7} + \left(\frac{1}{7} \div \frac{1}{3}\right)\right\}}= \frac{\left(\frac{16}{5} + \frac{3}{5}\right) \div \frac{8}{5}}{\frac{8}{7} \div \{\frac{5}{7}+\frac{3}{7}\}}$$

$$=\frac{\frac{19}{5}\div\frac{8}{5}}{\frac{8}{7}\div\frac{8}{7}}$$

$$=\frac{19}{5}\div\frac{8}{5}$$

$$=\frac{19}{8}$$

Hence, the correct answer is Option C