I know this is an older thread but I looked it up for help with a pushed-in tweeter dust cap on a pair of speakers I just received and wanted to add another technique that I discovered worked well.
I tried the vacuum cleaner hose trick, which had worked for me before, but it didn't have any effect on this one. Then I tried the adhesive tape suggestion, using the blue painter's masking tape that's designed not to leave a residue, and that pulled out most of the dent but left a small dimple that didn't respond even to the french-kiss technique.
As a last resort, I used a hair dryer on the low setting to gently heat the dust cap and the remaining small dimple came right out.
I don't know if it would have worked on the larger dent but I'd be tempted to try it first in the future since there's no physical contact with the dust cap and it's pretty easy to make sure you're not applying too much heat.
I tried the vacuum cleaner hose trick, which had worked for me before, but it didn't have any effect on this one. Then I tried the adhesive tape suggestion, using the blue painter's masking tape that's designed not to leave a residue, and that pulled out most of the dent but left a small dimple that didn't respond even to the french-kiss technique.
As a last resort, I used a hair dryer on the low setting to gently heat the dust cap and the remaining small dimple came right out.
I don't know if it would have worked on the larger dent but I'd be tempted to try it first in the future since there's no physical contact with the dust cap and it's pretty easy to make sure you're not applying too much heat.