There isn’t a way to avoid the “blips” of the colour change on the wrong side of your work, but there is a way to conceal them.
If you knit your scarf in reasonably dense ribbing, becuase the ribbing pulls together, only the knitted rib faces will show. The purl blips will still be there, but they will be hidden in the purl ditches.
Have a look at this striped scarf, for instance. It is knitted in 1x1 ribbing, but it looks like stockinette.
There’s no way to conceal the blips in garter stitch, except by keeping them all to one side and arranging your scarf so that side doesn’t show when you wear it.
P.S. The scarf that you want to make will probably look great with stripes in the loose garter stitch used. I would say “embrace the blips”, but of course it is your knitting and up to you to decide whether you would like the look or not.
Rather than trying to avoid the dash marks of the colour change I like to use them as a design feature.
Either accepting they are where they are, or making a stripe with even more of them by changing the colour more often making a band of both colours before eventually dropping colour A and making a solid stripe with B. Switching between A and B every 2 rows for a while would make an interesting colour pattern.
Or you could alter the stitch you use, not garter but say 2 rows knit, 2 rows purl. The 2 rows purl are in effect a reverse garter and give a similar overall effect but a colour change can then be placed on the 2 rows of knit meaning no purl bump dash marks on the right side. This though would be “better” on a top or hat where the wrong side is not seen. On a scarf both sides are seen so I’d prefer to make use of the colour change dashes by incorporating them into the design as a feature.
Another way to create colour design could be to work with 2 strands of A for a wide stripe, switch to 1 strand A and 1 strand B to work together for a stripe, then switch to 2 strands of B. Later working a B and C stripe, then all C etc.
Maybe try out your colours on a swatch to see how the different effect work and embrace the dashes?