Do I need special expensive 2-way glass polish (2x 0,5gr for ~$17) for a Smartphone, or cheaper?

[Tobias Claren]

Hello.

I need a polish solution for a Note 4 smartphone.
There is a visible scratch, if the phone is active.

There are expensive glas polish sets (for wathces, smartphones etc.) with two 0,5gr syringes with a grey paste for ~$17 (~€14).
Is this the best solution, or are there other cheaper polishes with the same effect?
Polishes for car glasses is only one paste, for example ~250gr "SONAX 02731410 PROFILINE GlassPolish Glas Scheiben Politur 250ml" for ~$20.
But only one liquid paste.

 

[Rukbat]

The best solution is no solution - don't use a glass polish on a phone. We used to do that (remove tiny surface scratches) using toothpaste (it's a very fine abrasive), but unless you've learned the technique (by trying it dozens of times on bad screens), you'll usually change the scratch, which is barely noticeable, into a large area of haze, which is glaringly obvious.