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Unfortunately, Typekit doesn't have all fonts. So, if your image came in with a font that's not installed on your computer, it's giving you that option - IF the font is available in Typekit, and if Typekit doesn't have that font, it's offering alternatives (looks like it knows it's replacing a sans serif font, so it's offering you it's most popular). My recommendation would be to choose "Don't Resolve". Then, go to Typekit (Type Menu>Add Fonts from Typekit) and try to find a variation on the font, or an alternative font of your choosing with which to replace the missing font. Then, you can sync directly from Typekit to your computer and replace the text.
If it's a REALLY specific font, or something funky, I recommend getting the actual font from the person who created the document.
Thank you very much. That's quite a helpful response. Appreciate your clarity and specific input.
Glad it helped!