Not clear that this is an Omega, but the module can be serviced if you can find someone willing to do it. Whoever you take it to, make sure they have worked with MOP dials before, because they do require some special handling. The dial can be cracked very easily for example during hand removal (in particular on a chronograph where the hands are on very tightly).
The fact that adhesive has been used is not a good sign. The manufacturer may be your best bet...
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