I control four creatures: C1 is enchanted by Fencer's Magemark, C2 is enchanted by another aura, C3 and C4 aren't enchanted. I use Phyrexian Splicer's ability to let C2 lose first strike and C3 gain first strike. Then I use Aura Finesse to move Fencer's Magemark to C4.

According to CR 613.6d an aura receives a new timestamp when attached to a new creature. According to CR 613.6a the continuous effect generated by its static ability has the same timestamp as the aura.

Does that mean that C2 regains first strike (so that the enchanted creatures C2 and C4 have first strike due to Fencer's Magemark and C3 has first strike due to Phyrexian Splicer)?

C2 regains first strike.

613.6d is a specific case for the whole rule. You always use it for Auras, so it receives a new timestamp when moved.

Daniel Kitachewsky
L3, Paris, France
Rules NetRep