I understand the meaning of sentence in the title as "please forgive (me) for just this." Is this understanding correct?
What exactly is the logical role of だけ here? 「これだけ」 or "only this" means an upper bound: this and nothing else. Why would anyone wish for forgiveness for one thing only and nothing else? Wouldn't you want to say "at least" rather than "only"?
Without further context, this sounds more like "Let me at least do this." 許して has dual meanings: "allow me" and "forgive me". Context here is extremely important to get the right gist and to understand why だけ could make sense.
A further thought. Suppose someone were accused on multiple counts. Perhaps the accused feels unjustly condemned, the accused might then request that at least one of these counts be forgiven, the one the accused feels most unjustly condemned on.
I'm not sure why A.Ellett's answer is downvoted.
The original question seems to be missing the point that the sample is これだけは and not これだけ.
As for the question, the original poster gets it right: これだけは indicates a lower bound. Thus これだけは許してください means Let me keep at least this / Let me do at least this.
It depends on the context but the phrase is most typically used for begging a permission rather than forgiveness. For example, you are in debt and the creditor takes your things away for compensation, one by one. Then he put his hand on your cherished book, then you beg with the phrase that he shouldn't take that way and let you keep it.
Another example: If a group of bandits raiding your house and starts wantonly killing your family members. Then you hold your kids and say この子たちだけは許してください, meaning Save these kids at least. This is more for forgiveness.
The use of だけ in some expressions in Japanese is not exactly logical/intuitive to learners coming from an English language background. For example: The expression 「できるだけ」 actually means "as much as one can",
however if you try to think logically and break into two words できる = can/be able to . だけ = only . So it ends up getting (mistakenly) translated as "ONLY as much as one can" (i.e, if your threshold is 80%, then ONLY do 80%. No need to beat yourself up over it).
I can totally understand your feeling of uneasiness at the lack of grammatical logic here, but the only way to get over it is to use it (and listen to people using it) until it starts to 'feel' natural.
