Step 1: Understand the question.
We must find the disease that is NOT sexually transmitted among the four given.
Step 2: Check genital warts.
Genital warts are caused by Human Papillomavirus and spread through sexual contact, so it is a sexually transmitted infection.
Step 3: Check syphilis.
Syphilis is caused by Treponema pallidum and spreads through sexual contact with lesions, so it is sexually transmitted.
Step 4: Check gonorrhoea.
Gonorrhoea is caused by Neisseria gonorrhoeae and affects the urogenital tract, spreading sexually, so it is an STI.
Step 5: Check tuberculosis.
Tuberculosis is caused by Mycobacterium tuberculosis and spreads mainly through airborne droplets when an infected person coughs or sneezes, not through sexual contact.
Step 6: Conclude.
Tuberculosis is the one that is not sexually transmitted.
\[ \boxed{\text{Tuberculosis}} \]