For me, a "background" skill is something you've picked up outside of whatever service/career you go into. It represents your daily living outside of that career and prior to that career.
Same here, IMTU “Background” skills are those you’ve learned prior to age 18, or after you roll stats but before you begin your Education or Career (using MgT 2e these days). However in MgT there’s just a list of skills to choose from, without any ties to who or what the character is.
Thus IMTU I have two tables, Birthworld (pretty self-explanatory but can include being born on an orbital station or on a ship) and also Upbringing (a simple one-word description of the character’s life growing up). The two tables lead to a selection of 0 level skills to primarily provide character depth for role play but also possibly in-game connections or adventure hooks as well.
Regarding “losing” that 0 level Background skill because later your Basic Training includes it, I always allow it to bump up to level 1. But kilemall’s suggestion of +1DM to commission/advancement rolls would be welcome at my table too. For MgT perhaps a +1DM to Qualification rolls would also work.