Heatsink on underside of PCB
This link contains useful information, also this video.

Typical solder mask has 20-25µm thickness and 0.2 W/m.K thermal conductivity. This means a 1cm2 area of solder mask will have a thermal resistance of 1°C/W. This can be a problem... or not, that depends on your application and how much power is dissipated. For a few watts, an extra 1°C/W doesn't matter, just do the calculation. For a larger contact area, thermal resistance drops accordingly.

However, soldermask has another very important role. If you use immersion gold, large copper areas without soldermask may result in a thick gold layer, and your PCB fab will be asking who's gonna pay for the extra gold. If you use HASL, solder thickness may not be even, which will require a thicker interface material to even out the bumps, and increase thermal resistance too. There could even be a little drop of solder left over on the edge of a via, and then your heat sink won't be flush, and if you try to remove the bump by hand, it'll make a mess. And of course, wave soldering would result in a mess too. So... soldermask is nice to have.

Anodized aluminium is insulated by the oxide layer, but it can get scratched off. So, a bare heat sink on top of vias with just conductive grease between them would work... in theory... still a bad idea. It's better to tent the vias and protect them with soldermask.

Thermal grease is better than silpads because it is thinner. However, silpads are insulating and thermal grease is not. Why not simply check the datasheet of your silpad and calculate the thermal resistance versus contact area, and check if it works?

Another option is a SMD heat sink. Pros: thermal conduction path is 100% metal. Cons: thermal path has to go horizontally through the copper layer, which isn't that efficient.

Anyway. If your IC only dissipates a few watts, keep the silkscreen or use a SMD heat sink.