= Solution
For the <Locality property of SLE>, take a <compact H-hull> $A$ away from $0$, and map $\mathbb H\setminus A$ conformally to $\mathbb H$ by $\psi_A$, fixing $0$ and infinity and with derivative one at infinity. Up to the first contact with $A$, the image under $\psi_A$ of an $\operatorname{SLE}_6$ grown in $\mathbb H$ has the same law as $\operatorname{SLE}_6$ grown in $\mathbb H$, after the change to its own <half-plane-capacity parameterization>. Equivalently, $\operatorname{SLE}_6$ in the smaller domain has the same initial law as the curve in the larger domain until the latter encounters the removed hull. There is no conditioning on eventual avoidance.
The <chordal restriction property> for $\operatorname{SLE}_{8/3}$ concerns the whole curve. Conditional on avoiding $A$, applying $\psi_A$ gives the original $\operatorname{SLE}_{8/3}$ law, modulo increasing reparameterization:
$$
\boxed{\mathcal L\bigl(\psi_A(\gamma)\mid\gamma\cap A=\varnothing\bigr)=\mathcal L(\gamma).}
$$
Its associated avoidance probability, from the <SLE eight-thirds restriction martingale>, is
$$
\boxed{\mathbb P(\gamma\cap A=\varnothing)=\psi_A'(0)^{5/8}.}
$$
Thus locality identifies a stopped, unconditioned law, whereas restriction identifies a conditioned law of the entire curve.
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