I have an experimental design that I did in 2 blocks (1 week apart). I'm struggling to understand how DESeq2 deals with covariates.

I checked a PCA and there is no clustering of blocks.

I've run a model

dds <- DESeqDataSetFromMatrix(countData = genes.matrix,
                                      colData = sample_info,
                                      design = ~ Group + block)

where block is coded as -0.5 and +0.5, with the idea that this should mean center the effects? But is this true? I've also coded as "B1" and "B2" but this has no impact on what DEGs are expressed.

How do I tell if block is having a significant influence on the overall results?

Would one interpret a significant result in group as occurring over and above variation in block? as you would in a regular linear model?

Any help appreciated!

If you add a nuisance variable, it will account for variation if it exists per gene, so usually the approach would be ~ batch + condition (this is in the vignette for example).

You should just keep batch as a factor, it will "average" over the levels of batch when estimating the condition effect. You don't need to code with the -.5 and +.5 to accomplish this.