I read the answer to this question Grammatical Pattern : VerbてのNoun but I do not see how it applies to the following sentence お申し込みにあたってのご注意
It cannot be "you must apply to be careful".
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The same idea still applies to your sentence (actually, it is not a complete sentence but a noun phrase). It is "notes on application" of somewhat polite and formal form.
To find out this, you should carefully analyze your sentence.
As you know, the noun 「お申し込み」 is 「お」 + 「申し込み」, "application."
One of the basic meanings of the next verb 「あたる」 is "to face".
As described in the answer in the question you linked, 「-ての」 followed by nouns express the condition. So 「お申し込みにあたっての」 is "when you face the application" or more naturally, "when you are making application."
Lastly, 「ご注意」 is 「ご」 + 「注意」. Here this is a noun rather than a verb (注意する), so it should be "notes" or "precautions," but not "to be careful."
Now, the interpretation of whole phrase is, "notes when you are making application."