Step 1: Understanding the Concept:
Milking hygiene and bovine lactation physiology: complete clean milking prevents mastitis and maximizes milk fat yield (strippings contain $>8-10\%$ fat), whereas foremilk is discarded because it harbors heavy bacterial loads from the teat canal, not due to inherent off-flavor.
Step 2: Detailed Explanation:
1. Statement I: In clean milk production, 'complete milking' (stripping) must be practiced so that no residual milk is left in the cisterns. Leaving residual milk creates internal intramammary pressure that suppresses ongoing secretion, causes early drying off, reduces total fat yield (strippings contain the highest fat content, $8 - 12\%$), and strongly predisposes to clinical mastitis. Hence, Statement I is correct.
2. Statement II: The first few squirts of foremilk from each teat are discarded into a strip cup because the teat canal harbors high concentrations of environmental and commensal bacteria ($> 50,000\text{ cfu/mL}$) and to physically examine for mastitic flakes/clots, NOT because it imparts an 'unsavoury flavor'. Hence, Statement II is false.
Step 3: Final Answer:
Therefore, Statement I is correct but Statement II is false, matching option (C).