  We prove an infinite dimensional integration by parts formula on the law of
the modulus of the Brownian bridge $BB=(BB_t)_{0 \leq t \leq 1}$ from $0$ to
$0$ in use of methods from white noise analysis and Dirichlet form theory.
Additionally to the usual drift term, this formula contains a distribution
which is constructed in the space of Hida distributions by means of a Wick
product with Donsker's delta (which correlates with the local time of $|BB|$ at
zero). This additional distribution corresponds to the reflection at zero
caused by the modulus.
