Nope - you can't be the word police - people can say what they like.
Bits is short for bits and pieces - non specific small items that would take too long and be too boring to list - examples - napkins, poundland walnut whips, paper plates, small cheap filler type gifts, chocolate coins, one of those calenders you can put in your purse that are at the counter in card shops, fluffy topped pencils, a weird kind of 'Christmas jam' from B & M, reduced sprinkles to go on the top of cakes, fancy ice cream wafers that were bogof in tesco, soap even though you only use hand wash because it was on offer (10 for the price of 1) a plastic pill holder and a fold up tote bag from Savers, extra bacon and cheese just in case, packs of plain biscuits (B&M again) in case anyone wants something less rich, a toilet duck, a milkpan with a wobbly handle, a large pack of wrapping paper just in case (in case you want to wrap everything you own until the year 2020), a dot to dot book and a packet of biros.
These are bits. 'Things' are items you went out to get and came home with, you can name them is questioned. Bits always surprise you when you get home because you don't really recall buying them, you just know you went out and got some bits.