Basis risk is nothing to do with the yield curve (which is why I do not mention it when discussing the yield curve in my lectures).
Basis risk relates to interest rate futures. Futures prices differ from actual interest rates and the difference is called the basis. For calculations on futures (which are not asked in Paper FM – only in Paper AFM) we assume that the difference falls linearly over the life of the future. In practice it might not fall in that way and that is what we call the basis risk.