I'd probably leave them as is. They tell more of a story together on piece. Since neither is in great condition, once you remove them you'll just have two dirty, damaged copies of a common stamp.
BTW, I believe both the circular cancels and the handstamp say "Butzbach (Oberhess)"
Paper seems to have a large amount of active mold on it + other (known and unknown) saprophytes... possible the best solution will be to burn it in the flame.
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