This also may be degeraded Dna not rna alone

Genomic dna shearded during the extraction that is normal thing particulary if you use mechanical destruption of cells

The important thing in this photo you have most of intact DNA so your PCR will work fine

But if you still need to minimze the degradtion try this

Use fresh sample for Dna extraction instead of frozen stroaged one

Try to perform the hemognization in ice

Add more protienase K to inhibit Danse

Or try to use beads for extraction

I agree that the abundant low molecular weight fraction could be degraded DNA. Be careful when using lyophilized material as a source since substantial DNA degradation may occur during the process of lyophilization especially in tissues with high content of nucleases. You may wish to isolate DNA from fresh leaf and see if a similar troubled band is still present or not.

If your low molecular weight band is RNA which can still be even after the RNAse A treatment (the enzyme does not cut RNA into nucleotides but rather to short fragments) you may wish to check a UV spectrum of your samples using a nanodrop. IF RNA is present the OD260/280 would be about 1.9-2.0. If it is DNA the ratio would be 1.7-1.8.

Good luck,

Ales