"用语" in this context can be translated as "phrase" or "expression". "信末署名前用语" can thus be translated as "the phrase/expression used before the signature at the end of a letter".
For a more concise and commonly used expression in English correspondence, you might also hear it referred to as "the complimentary close" (though this typically refers to the entire closing section, including the phrase and the signature line), or specifically describe it as "the phrase preceding the signature" in a letter.
If focusing strictly on the phrase part before the signature, "the pre-signature phrase" could also be a fitting translation, though it's less commonly used in everyday English compared to the descriptive phrases above.
In most practical contexts, simply explaining it as "the phrase used right before signing the letter" would be clear and effective.