I've heard it a lot in spoken language when a Boss says:
We object to get improved the quality of our products.
But, I think it should be:
We object to getting improved the quality our products.
As RichF mentions in his comment, neither is correct.
There is a difference between "I (or someone) objects to something" (using "object" as a verb), and saying something is the object (short for objective) of something like a task or a job (which is what I think you are trying to say).
The boss said that the object of the weekly meetings was to ensure good communication between workers and management.
The boss said, "Our object is to improve the quality of our products."
Again, here "object" can be used interchangeably with "objective", so if you are worried about causing confusion with the verb "to object" (or other meanings of "object), just use "objective". For example:
Our objective this quarter is to increase traffic to our website.
'We object to getting improved' is perfectly fine because 'object to + gerund' is a fixed structure, but it's never followed by an infinitive. E.g. • Tom objected to being in agreement with me last night because he is was radicalizing someone else.