Yes, meditation can be an object that we become attached to, but it does not have to be. Unfortunately, it is possible to become attached to, or base our self-identity on, all manner of things so it is good to develop the skill of recognizing this tendency and observe when it happens. Best is to recognize the self-cherishing thought as it arises and to get familiar with this enemy in order to eventually banish it.
Imagine you were in an industrial kitchen standing next to many very hot pans cooking on many hot stove tops. A small child is standing next to you. Imagine this child had a nasty habit of reaching out and touching these hot pans. The child cries as it is burnt and tips over the pans and makes a huge mess that can cause others to slip and fall. You would be well advised to try and control this child from hurting itself and others, right?
In just the same way we should try and control our minds from causing suffering for our self and others with non-virtuous thoughts and train in being mindful.
Similarly, we would like to gain a calm and pure mind. So we meditate. Isn't it a desire? (like wearing make-up for the mind?).
Is this workout (for the mind) a kind of attachment and if so is it a good thing?
It depends upon your motivation. If you are trying to calm your mind so that others will think highly of you or to impress others with how awesome your mental discipline is and become attached to the praise you receive, then yes this can be a form of attachment and non-virtuous. However, if your motivation is to reduce or eliminate the suffering of yourself and others, then I would say this is beneficial and virtuous. Keep going!
Isn't that a seeming contradiction since we are instructed to abandon attachments?
It is only a seeming contradiction if you think of this in a very stilted and artificial way. Still, it is possible to get attached to even virtuous practices. The reality is that for us lowly beings all practices are likely stained - at least in part - with the self-cherishing thought and impure motivations. So the best thing to do is try and reduce these thoughts and try to work slowly, slowly to adopting more altruistic motivations. There are benefits to controlling the mind from non-virtuous thoughts and developing this habit regardless if we have partially stained motivation.
Hope this helps!