This gift's for you
is fine, and seems appropriate for a message on a t-shirt.
Depending on the exact situation, however, it may be more common and natural to write:
A gift for you
meaning This is a gift for you.
It is likely that a teacher or textbook gave a suggestion, guideline, or rule not to use 's with a noun in order to prevent learners from using it to make a plural form.
He borrowed some book's from the library.
He borrowed some books' from the library.
Or, as you mentioned, to attempt to teach that 's is commonly used to indicate possession, not to make plural forms.
But we can use 's after most singular nouns to mean [noun] + is/has.
This book's very good. This book's been damaged.
We normally use these examples in speech, or written expression of dialogue. But in most writing we normally do not use these particular contractions. We spell them out:
This book is very good. This book has been damaged.
A single line printed on something as a promotion, however, is a special use, where this kind of contraction is common.